Constructs C^α self-similar blowup profiles for 3D Euler vorticity without swirl and proves asymptotically self-similar blowup from C_c^α data, with limiting factorization as α→(1/3)^-.
From instability to singularity formation in incompressible fluids
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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2026 9representative citing papers
Global regularity proven for 2D Boussinesq with fractional dissipation in subcritical regime α + β > 1 when α ≤ 2/3.
Constructs C^∞ self-similar blowup profiles for 1D models of 3D Euler at α=1/3 using fixed-point around a numerical approximation, plus nearby exact profiles for α slightly below 1/3.
Finite-time Type-I blowup is proved for 3D axisymmetric no-swirl Euler with C^{1,α} finite-energy data for every α < 1/3 via a Lagrangian clock-and-driver mechanism.
Introduces a matrix-clock criterion and reduces it to a scalar clock inequality that rules out finite-time collapse of the deformation gradient for conditional C^{1,α} axisymmetric Euler solutions when α ≥ 1/3.
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
A unified polar subsystem of 2D Boussinesq and 3D axisymmetric Euler yields exact (1+1)D axis reductions whose apex obeys a CLM-type ODE and blows up in finite time.
Finite-time vorticity blow-up is shown to exist for the forced 2D non-homogeneous Euler equations via adaptation of a prior Boussinesq construction.
G-invariant divergence-free initial data on compact cohomogeneity-one manifolds yield global smooth G-invariant solutions to the incompressible Euler equations.
citing papers explorer
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Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity II: 3D Profiles, Blowup, and Limiting behavior
Constructs C^α self-similar blowup profiles for 3D Euler vorticity without swirl and proves asymptotically self-similar blowup from C_c^α data, with limiting factorization as α→(1/3)^-.
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Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation
Global regularity proven for 2D Boussinesq with fractional dissipation in subcritical regime α + β > 1 when α ≤ 2/3.
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Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity I: $C^{\infty}$ 1D Limiting Profiles
Constructs C^∞ self-similar blowup profiles for 1D models of 3D Euler at α=1/3 using fixed-point around a numerical approximation, plus nearby exact profiles for α slightly below 1/3.
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Incompressible Euler Blowup at the $C^{1,\frac{1}{3}}$ Threshold
Finite-time Type-I blowup is proved for 3D axisymmetric no-swirl Euler with C^{1,α} finite-energy data for every α < 1/3 via a Lagrangian clock-and-driver mechanism.
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A conditional Lagrangian clock barrier at the $C^{1,\frac{1}{3}}$ threshold for axisymmetric Euler without swirl
Introduces a matrix-clock criterion and reduces it to a scalar clock inequality that rules out finite-time collapse of the deformation gradient for conditional C^{1,α} axisymmetric Euler solutions when α ≥ 1/3.
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A unified Boussinesq--Euler formulation and finite-time blow-up for a Hou--Luo type boundary-jet system
The authors unify the Boussinesq and axisymmetric Euler systems into a parameterized boundary-jet model and prove finite-time blow-up for its closed truncation using a Riccati argument.
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2D inviscid Boussinesq equations and 3D axisymmetric Euler equations: (1) A unification ($Em$), (2) Finite-time blow-up of two unified $(1+1)$D systems rigorously derived from ($Em$)
A unified polar subsystem of 2D Boussinesq and 3D axisymmetric Euler yields exact (1+1)D axis reductions whose apex obeys a CLM-type ODE and blows up in finite time.
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Vorticity blow-up for the 2D incompressible non-homogeneous Euler equations with uniform $C^{1,\sqrt{\frac{4}{3}}-1-\varepsilon}$ force
Finite-time vorticity blow-up is shown to exist for the forced 2D non-homogeneous Euler equations via adaptation of a prior Boussinesq construction.
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Incompressible Euler fluids on compact cohomogeneity one manifolds
G-invariant divergence-free initial data on compact cohomogeneity-one manifolds yield global smooth G-invariant solutions to the incompressible Euler equations.