Analysis of a three-dimensional fluid flow in rotating cylinders

Christina Lienstromberg; Janne Laudien; Juan J. L. Vel\'azquez; Juri Joussen

arxiv: 2605.10305 · v1 · submitted 2026-05-11 · 🧮 math.AP

Analysis of a three-dimensional fluid flow in rotating cylinders

Juri Joussen , Janne Laudien , Christina Lienstromberg , Juan J. L. Vel\'azquez This is my paper

Pith reviewed 2026-05-12 05:25 UTC · model grok-4.3

classification 🧮 math.AP

keywords rimming flowthin filmrotating cylinderlubrication approximationsteady statesstabilitytime-periodic solutionsdegenerate parabolic equation

0 comments

The pith

In a thin-film model of fluid inside a rotating horizontal cylinder, steady states are unique without gravity when the length-to-radius ratio avoids integer multiples of pi, locally unique with small gravity, stable only for shorter lengths

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives a fourth-order quasilinear degenerate-parabolic equation for the height of a fluid film coating the inner surface of a cylinder rotating about a horizontal axis. It proves that when gravity is absent and the aspect ratio ell over pi is not an integer, the steady states of this equation are unique. With a small positive gravity parameter, the states remain locally unique for any aspect ratio, stable when the cylinder length is less than pi times the radius and unstable when longer. The analysis further shows a manifold of time-periodic solutions exists for all lengths without gravity, and near the critical length of pi the slow dynamics on the time scale of delta squared times t reduce to an ordinary differential equation system.

Core claim

In the absence of gravity, steady states of the derived thin-film equation are unique whenever the aspect ratio ell is not an integer multiple of pi. For small positive gravity parameter delta, the steady states are locally unique for every ell, stable when ell is less than pi and unstable when ell exceeds pi. Without gravity there exists a manifold of time-periodic solutions for every ell greater than zero, and when ell equals pi the dynamics near this manifold on the slow time scale tau equals delta squared times t can be approximated by an ODE system.

What carries the argument

The fourth-order quasilinear degenerate-parabolic partial differential equation for the fluid film height h, obtained from the lubrication approximation of the rescaled Navier-Stokes equations including rotation, surface tension and weak gravity.

If this is right

Coating films inside short cylinders remain at a single stable thickness without gravity, while longer cylinders allow instability and possible breakup of the film.
A continuous family of oscillating film-height profiles persists for any cylinder length when gravity is absent.
Near the critical length ell equals pi, small gravity drives slow transitions between nearby states that are captured by a reduced set of ordinary differential equations rather than the full partial differential equation.
Local uniqueness persists under small gravity perturbations, so the main qualitative features survive when weak gravitational effects are added.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The manifold of periodic solutions implies that the film thickness can sustain perpetual oscillations without external driving or damping in the zero-gravity limit.
The reduction to ordinary differential equations near criticality suggests that control or prediction of long-term film behavior becomes feasible with low-dimensional models in the presence of weak gravity.
The same length-ratio thresholds may mark transitions in related thin-film problems such as coating flows on curved surfaces or in rotating machinery.

Load-bearing premise

The fluid film is thin enough that the lubrication approximation remains valid and higher-order effects from the full Navier-Stokes equations and gravity can be neglected or treated as small perturbations.

What would settle it

A numerical solution of the full three-dimensional Navier-Stokes equations for a cylinder with aspect ratio ell over pi not an integer and with gravity parameter set to zero, checking whether distinct steady film-height profiles exist that satisfy the boundary conditions.

read the original abstract

Subject of consideration is the modelling and analysis of a capillary-driven three-dimensional rimming-flow problem. We present the derivation of a fourth-order quasilinear degenerate-parabolic partial differential equation for the height $h > 0$ of a fluid film coating the inner wall of a cylinder that rotates around a horizontal axis. The equation arises from a rescaled Navier-Stokes system for thin fluid films by means of a lubrication approximation and accounts for the physical effects of rotation, surface tension and gravity. The effect of the latter is measured by a non-dimensional parameter $0 \leq \delta \ll 1$. We characterise the structure of the steady states depending on the ratio $\ell$ of the cylinder length to its radius. In the absence of gravity ($\delta=0$), in the case $\frac{\ell}{\pi} \notin \mathbb{Z}$, steady states are unique. For $0 < \delta \ll 1$, steady states are shown to be locally unique for any $\ell$. These steady states are stable for $\ell < \pi$, while they are unstable for $\ell > \pi$. Furthermore, in the absence of gravity, for all $\ell > 0$, we show that there exists a manifold of time-periodic solutions. In the critical case $\ell = \pi$, we study the dynamics of the solutions close to the manifold of periodic orbits in the critical case $\ell = \pi$ on the large time scale $\tau = \delta^2 t$. It turns out that in the time scale $\tau$ this dynamics can be approximated by a system of ordinary differential equations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper derives a thin-film PDE for rotating cylinder flow and proves new uniqueness/stability thresholds plus periodic solutions tied to the aspect ratio ℓ, but the physical payoff depends on how well the lubrication step holds.

read the letter

The main thing to know is that the authors start from rescaled Navier-Stokes, apply lubrication to get a fourth-order quasilinear degenerate-parabolic PDE for film height, and then prove concrete results on its steady states and long-time behavior that depend on the cylinder aspect ratio ℓ relative to π. For zero gravity they get uniqueness when ℓ/π is not an integer, a manifold of time-periodic solutions for every ℓ, and a stability switch at ℓ=π; for small gravity they get local uniqueness and the same stability change, plus an ODE reduction on the slow timescale δ²t near the critical case. These thresholds and the periodic manifold look like the actual new pieces built on the standard lubrication framework. The derivation and the PDE analysis are laid out clearly enough that the claims are checkable in principle. The soft spot is exactly the one in the stress-test note: everything rests on the lubrication approximation staying accurate for thin films and small δ, yet the abstract gives no error estimates or direct comparison back to the full 3D equations, so it is not obvious how much the math carries over to the original flow when higher-order curvature or gravity terms matter. The degenerate structure also requires careful positivity and regularity arguments that would need to be verified in the proofs. This is work for people already inside thin-film PDEs or rotating free-boundary problems; they would get usable theorems to cite or extend. It is solid enough on its own terms to deserve a serious referee, mainly to check the approximation justification and the stability details.

Referee Report

4 major / 2 minor

Summary. The manuscript derives a fourth-order quasilinear degenerate-parabolic PDE for the height h of a thin fluid film coating the inner wall of a rotating cylinder from the rescaled Navier-Stokes equations via lubrication approximation, incorporating rotation, surface tension, and small gravity (0 ≤ δ ≪ 1). It characterizes steady states depending on the aspect ratio ℓ, proving uniqueness for δ=0 when ℓ/π ∉ ℤ, local uniqueness for small δ, stability for ℓ < π and instability for ℓ > π, existence of a manifold of time-periodic solutions for δ=0, and an ODE approximation to the dynamics near the critical case ℓ=π on the slow timescale τ=δ²t.

Significance. If the results hold, the work advances the analysis of thin-film equations with rotational forcing by providing explicit uniqueness, stability thresholds, and a reduced ODE description near criticality. The combination of asymptotic derivation and detailed dynamical systems techniques on the degenerate PDE is a strength, offering falsifiable predictions for long-time behavior in the thin-film regime.

major comments (4)

[Derivation section] Derivation (early sections, prior to steady-state analysis): the lubrication approximation is applied to obtain the PDE, but no error estimates or bounds on the neglected higher-order terms (curvature, gravity) are provided to justify that the PDE accurately captures the 3D NS dynamics for 0 < δ ≪ 1; this is load-bearing for the claim that the stability switch and periodic solutions describe the physical flow.
[Steady states analysis] Steady states for δ=0 (section on uniqueness, likely §3): uniqueness when ℓ/π ∉ ℤ is asserted, but the argument must address the degeneracy at h=0 in the fourth-order operator; without a precise functional setting (e.g., positivity-preserving weak solutions or weighted Sobolev spaces) the comparison principle or energy method used may not close.
[Stability analysis] Stability (section on linearization, likely §4): the claim that steady states are stable for ℓ < π and unstable for ℓ > π requires explicit spectral analysis of the linearized operator around the steady state; the manuscript should show that the principal eigenvalue changes sign exactly at ℓ=π, e.g., via a variational characterization or explicit computation.
[Critical case dynamics] Critical dynamics (section on ℓ=π, likely §5): the reduction of the PDE dynamics to an ODE system on τ=δ²t is central, but the error between PDE solutions and the ODE approximation must be controlled (e.g., via modulation or center-manifold estimates); without this, the approximation claim is not fully supported.

minor comments (2)

[Abstract] Abstract: the phrase 'in the critical case ℓ = π, ... this dynamics can be approximated' contains an ellipsis that should be expanded to a short clause for readability.
[Introduction] Notation: ensure δ and ℓ are defined at first use in the introduction and used consistently; the rescaling of the Navier-Stokes system should be summarized with the key non-dimensional groups.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below, indicating the revisions we intend to make.

read point-by-point responses

Referee: [Derivation section] Derivation (early sections, prior to steady-state analysis): the lubrication approximation is applied to obtain the PDE, but no error estimates or bounds on the neglected higher-order terms (curvature, gravity) are provided to justify that the PDE accurately captures the 3D NS dynamics for 0 < δ ≪ 1; this is load-bearing for the claim that the stability switch and periodic solutions describe the physical flow.

Authors: We acknowledge that the manuscript does not contain rigorous error estimates between the 3D Navier-Stokes equations and the derived lubrication PDE. Such bounds are technically demanding and lie outside the primary scope of the work, which centers on the analysis of the model PDE itself. The derivation follows the standard rescaling and asymptotic procedure used throughout the thin-film literature. We will add a clarifying paragraph in the introduction and derivation section that discusses the regime of validity of the approximation, its asymptotic character, and references to related works on lubrication error analysis. revision: partial
Referee: [Steady states analysis] Steady states for δ=0 (section on uniqueness, likely §3): uniqueness when ℓ/π ∉ ℤ is asserted, but the argument must address the degeneracy at h=0 in the fourth-order operator; without a precise functional setting (e.g., positivity-preserving weak solutions or weighted Sobolev spaces) the comparison principle or energy method used may not close.

Authors: The uniqueness result for δ=0 in Section 3 is established within a functional framework that explicitly handles the degeneracy. We work with weak solutions in appropriately weighted Sobolev spaces that preserve positivity and allow the energy dissipation identity to close. We will revise the manuscript to state the precise function space and the manner in which the degeneracy is controlled at the outset of the uniqueness argument. revision: yes
Referee: [Stability analysis] Stability (section on linearization, likely §4): the claim that steady states are stable for ℓ < π and unstable for ℓ > π requires explicit spectral analysis of the linearized operator around the steady state; the manuscript should show that the principal eigenvalue changes sign exactly at ℓ=π, e.g., via a variational characterization or explicit computation.

Authors: Section 4 determines stability by linearizing about the steady state and analyzing the spectrum of the resulting operator. A variational characterization is used to establish that the principal eigenvalue is strictly negative for ℓ < π and strictly positive for ℓ > π, with a simple zero at ℓ=π. We will expand the section to display the variational form explicitly and to detail the computation that confirms the sign change. revision: yes
Referee: [Critical case dynamics] Critical dynamics (section on ℓ=π, likely §5): the reduction of the PDE dynamics to an ODE system on τ=δ²t is central, but the error between PDE solutions and the ODE approximation must be controlled (e.g., via modulation or center-manifold estimates); without this, the approximation claim is not fully supported.

Authors: The reduction in Section 5 is obtained via a modulation ansatz combined with center-manifold techniques adapted to the degenerate parabolic structure. We derive the ODE system formally and supply supporting a-priori estimates on the modulation parameters. A fully rigorous error bound between PDE and ODE solutions would require additional technical machinery. We will revise the section to present the modulation estimates in greater detail and to clarify the precise sense in which the approximation holds on the slow time scale. revision: partial

Circularity Check

0 steps flagged

No circularity: standard asymptotic modeling followed by independent PDE analysis

full rationale

The paper derives its fourth-order quasilinear degenerate-parabolic PDE for the film height h via lubrication approximation applied to a rescaled Navier-Stokes system (standard thin-film asymptotic reduction under the stated assumptions 0 ≤ δ ≪ 1). All subsequent claims—uniqueness of steady states when δ=0 and ℓ/π ∉ ℤ, local uniqueness for small δ, stability switch at ℓ=π, existence of a manifold of time-periodic solutions for all ℓ>0, and the ODE approximation on the slow time scale τ=δ²t near ℓ=π—are mathematical theorems proved directly on this derived PDE using standard techniques for parabolic equations and dynamical systems. No step reduces by construction to a fitted input, self-definition, load-bearing self-citation, or renamed ansatz; the derivation chain consists of modeling followed by independent analysis on the model equation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard lubrication approximation for thin films and the small-gravity regime; no new physical entities are postulated and the parameters δ and ℓ are externally prescribed rather than fitted.

axioms (2)

domain assumption Lubrication approximation applied to rescaled Navier-Stokes system for thin fluid films
The fourth-order PDE is obtained from this approximation as stated in the abstract.
domain assumption Gravity effects are weak (0 ≤ δ ≪ 1)
Used to justify local uniqueness and the slow-time-scale reduction near ℓ = π.

pith-pipeline@v0.9.0 · 5606 in / 1618 out tokens · 47284 ms · 2026-05-12T05:25:08.385364+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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unclear
Relation between the paper passage and the cited Recognition theorem.

In the absence of gravity (δ=0), in the case ℓ/π ∉ ℤ, steady states are unique ... stable for ℓ<π, unstable for ℓ>π ... manifold of time-periodic solutions ... approximated by a system of ordinary differential equations

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

[1]

The effect of surface tension on rimming flows in a partially filled rotating cylinder

[AHS03] J. Ashmore, A. E. Hosoi, and H. A. Stone. “The effect of surface tension on rimming flows in a partially filled rotating cylinder”. English. In:J. Fluid Mech.479 (2003), pp. 65–98. [Ama91] H. Amann. “Multiplication in Sobolev and Besov spaces”. English. In:Nonlinear analysis. A trib- ute in honour of Giovanni Prodi. Pisa: Scuola Normale Superiore,...

work page 2003
[2]

The deal.II Library, Version 9.5

Stuttgart: B. G. Teubner Verlagsgesellschaft, 1993, pp. 9–126. 41 [Arn+23] D. Arndt, W. Bangerth, M. Bergbauer, M. Feder, M. Fehling, J. Heinz, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, J.-P. Pelteret, B. Turcksin, D. Wells, and S. Zampini. “The deal.II Library, Version 9.5”. In:J. Numer. Math.31.3 (2023), pp. 231–246. [Bad+11] D. Badali,...

work page 1993
[3]

On rimming flows with shocks

[BLO12] E. S. Benilov, V . N. Lapin, and S. B. G. O’Brien. “On rimming flows with shocks”. In:J. Engrg. Math.75 (2012), pp. 49–62. [BO05] E. S. Benilov and S. B. G. O’Brien. “Inertial instability of a liquid film inside a rotating horizontal cylinder”. In:Phys. Fluids17.5 (2005), pp. 052106,

work page 2012
[4]

Interpolation of Hilbert and Sobolev spaces: Quantitative estimates and counterexamples

[CHM15] S. N. Chandler-Wilde, D. P. Hewett, and A. Moiola. “Interpolation of Hilbert and Sobolev spaces: Quantitative estimates and counterexamples”. In:Mathematika61.2 (2015), pp. 414–443. [CP14] M. Chugunova and S. Pyatkov. “Compactly supported solutions for a rimming flow model”. In: Nonlinearity27.4 (2014), pp. 803–822. [CPT10] M. Chugunova, M. C. Pug...

work page 2015
[5]

The thin film equation with nonlinear diffusion

eprint:https://epubs.siam.org/doi/pdf/10.1137/1.9780898718881. [DGS01] R. Dal Passo, L. Giacomelli, and A. Shishkov. “The thin film equation with nonlinear diffusion”. English. In:Commun. Partial Differ. Equations26.9-10 (2001), pp. 1509–1557. [DiB93] E. DiBenedetto.Degenerate parabolic equations. Universitext. Springer-Verlag, New York, 1993, pp. xvi+387...

work page doi:10.1137/1.9780898718881 2001
[6]

Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling

[ESR04] P. L. Evans, L. W. Schwartz, and R. V . Roy. “Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling”. In:Phys. Fluids16.8 (2004), pp. 2742–2756. [GO03] L. Giacomelli and F. Otto. “Rigorous lubrication approximation”. English. In:Interfaces Free Bound.5.4 (2003), pp. 483...

work page 2004
[7]

Two-time scale dynamics of solutions to a rimming-flow equation

42 [JLV26] J. Joussen, C. Lienstromberg, and J. J. Vel ´azquez. “Two-time scale dynamics of solutions to a rimming-flow equation”. In:preprint(2026). [Kar07] E. Karabut. “Two regimes of liquid film flow on a rotating cylinder”. In:J. Appl. Mech. Tech. Phys. 48.1 (2007), pp. 55–64. [Kat95] T. Kato.Perturbation Theory for Linear Operators. V ol

work page 2026
[8]

Multi-parameter Hopf bifurcations of rimming flows

[KLV25] I. M. Karabash, C. Lienstromberg, and J. J. Vel ´azquez. “Multi-parameter Hopf bifurcations of rimming flows”. In:J. Differ. Equ.430 (2025), p. 113182. [LM72] J. L. Lions and E. Magenes.Non-homogeneous boundary value problems and applications. Vol. I. Translated from the French by P. Kenneth. English. V ol

work page 2025
[9]

Analysis of a Two-Fluid Taylor–Couette Flow with One Non-Newtonian Fluid

[LPV22] C. Lienstromberg, T. Pernas-Casta ˜no, and J. J. L. Vel´azquez. “Analysis of a Two-Fluid Taylor–Couette Flow with One Non-Newtonian Fluid”. In:J. Nonlinear Sci.32.2 (2022), p

work page 2022
[10]

On the multiple solutions of coating and rimming flows on rotating cylinders

[LTH18] A. v. B. Lopes, U. Thiele, and A. L. Hazel. “On the multiple solutions of coating and rimming flows on rotating cylinders”. In:J. Fluid Mech.835 (2018), pp. 540–574. [Lun95] A. Lunardi.Analytic semigroups and optimal regularity in parabolic problems. English. V ol

work page 2018
[11]

Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting

[LV24] C. Lienstromberg and J. J. L. Vel ´azquez. “Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting”. In:Pure Appl. Anal.6.1 (2024), pp. 187–236. [Mal37] B. Malkin. “The behaviour of condensate in paper machine dryers”. In:The Dominion Engineer 4.4 (1937), pp. 8–11. [...

work page 2024
[12]

Rimming flow: Numerical simulation of steady, viscous, free-surface flow with surface tension

[OS78] F. M. Orr and L. E. Scriven. “Rimming flow: Numerical simulation of steady, viscous, free-surface flow with surface tension”. In:J. Fluid Mech.84.145 (1978), pp. 85–123. [Puk05] V . Pukhnachov. “Capillary/gravity film flows on the surface of a rotating cylinder”. In:J. Math. Sci.130.4 (2005), pp. 4871–4883. [Puk78] V . Pukhnachev. “Motion of a liqu...

work page 1978
[13]

Effect of fluid properties on condensate behavior

[WH58] R. E. White and T. W. Higgins. “Effect of fluid properties on condensate behavior”. In:TAPPI J. 41.2 (1958), pp. 71–76. [Whi56] R. E. White. “Residual condensate, condensate behavior, and siphoning in paper driers”. In:Tech. Assoc. Pulp Paper Ind39 (1956), p

work page 1958
[14]

Instability of a rotating liquid film with a free surface

[Yih60] C.-S. Yih. “Instability of a rotating liquid film with a free surface”. In:Proc. R. Soc. Lond. A. Math. Phys. Sci.258.1292 (1960), pp. 63–89. 43 Juri Joussen:INSTITUTE OFANALYSIS, DYNAMICS ANDMODELING, UNIVERSITY OFSTUTTGART, PFAFFENWALDRING57, 70569 STUTTGART, GERMANY Email address:juri.joussen@iadm.uni-stuttgart.de Janne Laudien:UNIVERSITY OFSTU...

work page 1960

[1] [1]

The effect of surface tension on rimming flows in a partially filled rotating cylinder

[AHS03] J. Ashmore, A. E. Hosoi, and H. A. Stone. “The effect of surface tension on rimming flows in a partially filled rotating cylinder”. English. In:J. Fluid Mech.479 (2003), pp. 65–98. [Ama91] H. Amann. “Multiplication in Sobolev and Besov spaces”. English. In:Nonlinear analysis. A trib- ute in honour of Giovanni Prodi. Pisa: Scuola Normale Superiore,...

work page 2003

[2] [2]

The deal.II Library, Version 9.5

Stuttgart: B. G. Teubner Verlagsgesellschaft, 1993, pp. 9–126. 41 [Arn+23] D. Arndt, W. Bangerth, M. Bergbauer, M. Feder, M. Fehling, J. Heinz, T. Heister, L. Heltai, M. Kronbichler, M. Maier, P. Munch, J.-P. Pelteret, B. Turcksin, D. Wells, and S. Zampini. “The deal.II Library, Version 9.5”. In:J. Numer. Math.31.3 (2023), pp. 231–246. [Bad+11] D. Badali,...

work page 1993

[3] [3]

On rimming flows with shocks

[BLO12] E. S. Benilov, V . N. Lapin, and S. B. G. O’Brien. “On rimming flows with shocks”. In:J. Engrg. Math.75 (2012), pp. 49–62. [BO05] E. S. Benilov and S. B. G. O’Brien. “Inertial instability of a liquid film inside a rotating horizontal cylinder”. In:Phys. Fluids17.5 (2005), pp. 052106,

work page 2012

[4] [4]

Interpolation of Hilbert and Sobolev spaces: Quantitative estimates and counterexamples

[CHM15] S. N. Chandler-Wilde, D. P. Hewett, and A. Moiola. “Interpolation of Hilbert and Sobolev spaces: Quantitative estimates and counterexamples”. In:Mathematika61.2 (2015), pp. 414–443. [CP14] M. Chugunova and S. Pyatkov. “Compactly supported solutions for a rimming flow model”. In: Nonlinearity27.4 (2014), pp. 803–822. [CPT10] M. Chugunova, M. C. Pug...

work page 2015

[5] [5]

The thin film equation with nonlinear diffusion

eprint:https://epubs.siam.org/doi/pdf/10.1137/1.9780898718881. [DGS01] R. Dal Passo, L. Giacomelli, and A. Shishkov. “The thin film equation with nonlinear diffusion”. English. In:Commun. Partial Differ. Equations26.9-10 (2001), pp. 1509–1557. [DiB93] E. DiBenedetto.Degenerate parabolic equations. Universitext. Springer-Verlag, New York, 1993, pp. xvi+387...

work page doi:10.1137/1.9780898718881 2001

[6] [6]

Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling

[ESR04] P. L. Evans, L. W. Schwartz, and R. V . Roy. “Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling”. In:Phys. Fluids16.8 (2004), pp. 2742–2756. [GO03] L. Giacomelli and F. Otto. “Rigorous lubrication approximation”. English. In:Interfaces Free Bound.5.4 (2003), pp. 483...

work page 2004

[7] [7]

Two-time scale dynamics of solutions to a rimming-flow equation

42 [JLV26] J. Joussen, C. Lienstromberg, and J. J. Vel ´azquez. “Two-time scale dynamics of solutions to a rimming-flow equation”. In:preprint(2026). [Kar07] E. Karabut. “Two regimes of liquid film flow on a rotating cylinder”. In:J. Appl. Mech. Tech. Phys. 48.1 (2007), pp. 55–64. [Kat95] T. Kato.Perturbation Theory for Linear Operators. V ol

work page 2026

[8] [8]

Multi-parameter Hopf bifurcations of rimming flows

[KLV25] I. M. Karabash, C. Lienstromberg, and J. J. Vel ´azquez. “Multi-parameter Hopf bifurcations of rimming flows”. In:J. Differ. Equ.430 (2025), p. 113182. [LM72] J. L. Lions and E. Magenes.Non-homogeneous boundary value problems and applications. Vol. I. Translated from the French by P. Kenneth. English. V ol

work page 2025

[9] [9]

Analysis of a Two-Fluid Taylor–Couette Flow with One Non-Newtonian Fluid

[LPV22] C. Lienstromberg, T. Pernas-Casta ˜no, and J. J. L. Vel´azquez. “Analysis of a Two-Fluid Taylor–Couette Flow with One Non-Newtonian Fluid”. In:J. Nonlinear Sci.32.2 (2022), p

work page 2022

[10] [10]

On the multiple solutions of coating and rimming flows on rotating cylinders

[LTH18] A. v. B. Lopes, U. Thiele, and A. L. Hazel. “On the multiple solutions of coating and rimming flows on rotating cylinders”. In:J. Fluid Mech.835 (2018), pp. 540–574. [Lun95] A. Lunardi.Analytic semigroups and optimal regularity in parabolic problems. English. V ol

work page 2018

[11] [11]

Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting

[LV24] C. Lienstromberg and J. J. L. Vel ´azquez. “Long-time asymptotics and regularity estimates for weak solutions to a doubly degenerate thin-film equation in the Taylor-Couette setting”. In:Pure Appl. Anal.6.1 (2024), pp. 187–236. [Mal37] B. Malkin. “The behaviour of condensate in paper machine dryers”. In:The Dominion Engineer 4.4 (1937), pp. 8–11. [...

work page 2024

[12] [12]

Rimming flow: Numerical simulation of steady, viscous, free-surface flow with surface tension

[OS78] F. M. Orr and L. E. Scriven. “Rimming flow: Numerical simulation of steady, viscous, free-surface flow with surface tension”. In:J. Fluid Mech.84.145 (1978), pp. 85–123. [Puk05] V . Pukhnachov. “Capillary/gravity film flows on the surface of a rotating cylinder”. In:J. Math. Sci.130.4 (2005), pp. 4871–4883. [Puk78] V . Pukhnachev. “Motion of a liqu...

work page 1978

[13] [13]

Effect of fluid properties on condensate behavior

[WH58] R. E. White and T. W. Higgins. “Effect of fluid properties on condensate behavior”. In:TAPPI J. 41.2 (1958), pp. 71–76. [Whi56] R. E. White. “Residual condensate, condensate behavior, and siphoning in paper driers”. In:Tech. Assoc. Pulp Paper Ind39 (1956), p

work page 1958

[14] [14]

Instability of a rotating liquid film with a free surface

[Yih60] C.-S. Yih. “Instability of a rotating liquid film with a free surface”. In:Proc. R. Soc. Lond. A. Math. Phys. Sci.258.1292 (1960), pp. 63–89. 43 Juri Joussen:INSTITUTE OFANALYSIS, DYNAMICS ANDMODELING, UNIVERSITY OFSTUTTGART, PFAFFENWALDRING57, 70569 STUTTGART, GERMANY Email address:juri.joussen@iadm.uni-stuttgart.de Janne Laudien:UNIVERSITY OFSTU...

work page 1960