Establishes refined L^p-based blow-up criteria for triangular SKT cross-diffusion systems via hierarchical structure and tame Sobolev estimates, and proves global existence of non-negative strong solutions for two-species logistic systems in d ≤ 2.
Fourier analysis and nonlinear partial differential equations , SERIES =
16 Pith papers cite this work, alongside 2,878 external citations. Polarity classification is still indexing.
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Short-time well-posedness established for two-phase Muskat problem with surface tension in log-critical regularity without RT condition, via new Schauder estimates for transmission problems in moving domains.
Proves temporal convergence rate of almost 1 for stochastic-convolution-based approximations of nonlinear 1+1D SPDEs with additive space-time white noise, improving on the optimal 1/4 rate for Wiener-increment schemes.
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
Kernel-adapted Schauder estimates in critical Hölder/Besov spaces yield local and global well-posedness for the Muskat equation with surface tension and Peskin problems with nonlinear elastic tension.
Global existence of H¹ martingale solutions to the stochastic Camassa-Holm equation is shown via viscous Galerkin approximations, tightness, and Skorokhod-Jakubowski representations.
Proves almost sure continuous dependence of the solution map on initial data in H^s (s>3/2) and existence of non-unique invariant measures for the Camassa-Holm equation with linear multiplicative noise.
Global solutions to Navier-Stokes with Coriolis force decay at linearized rates, faster than heat flow, in L^p norms for p in [2, infinity] when initial data is small.
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
Global smooth solutions exist for small data in the viscous β-plane equations, with decay faster than the heat equation and asymptotic behavior matching the linear kernel.
If a mild solution to 3D incompressible Navier-Stokes with v0 in Ḣ^{1/2} and Ω0 in L^{r0} (r0∈(1,2)) blows up at T*, then for any 2<p<∞ and unit vector e the integral ∫_0^{T*} ||(v(t)|e)||_{Ḃ^{1/2+2/p}_{2,∞}}^p dt diverges at T*.
Establishes local strong solutions and conditional global solutions for 3D inhomogeneous NS with data in C¹ × (L² ∩ VMO^{-1}) using density transport regularity and a new freezing-coefficient approach for momentum.
A Beale-Kato-Majda Lipschitz control on density and velocity gradients with strong time integrability, combined with material acceleration estimates, yields a continuation criterion and weak-strong uniqueness for the compressible fluid-viscoelastic shell system.
These lecture notes assemble the standard Wiener-chaos toolbox — Hermite polynomials, Wick calculus, the Gaussian free field, and Φ⁴ renormalisation — for a summer-school audience.
citing papers explorer
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Refined blow-up criteria and global solutions for triangular cross-diffusion systems
Establishes refined L^p-based blow-up criteria for triangular SKT cross-diffusion systems via hierarchical structure and tame Sobolev estimates, and proves global existence of non-negative strong solutions for two-species logistic systems in d ≤ 2.
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Schauder-type Estimates and Log-Critical Well-posedness for the Two-Phase Muskat Problem with Surface Tension
Short-time well-posedness established for two-phase Muskat problem with surface tension in log-critical regularity without RT condition, via new Schauder estimates for transmission problems in moving domains.
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Higher order approximation of nonlinear SPDEs with additive space-time white noise
Proves temporal convergence rate of almost 1 for stochastic-convolution-based approximations of nonlinear 1+1D SPDEs with additive space-time white noise, improving on the optimal 1/4 rate for Wiener-increment schemes.
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Kinetic Fokker-Planck Equations with Nonlinear Diffusion
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
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Weyl asymptotic formulas in the nilpotent Lie group setting
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Schauder-type Estimates and Well-posedness for Nonlocal Quasilinear Evolution Equations in Fluid Dynamics
Kernel-adapted Schauder estimates in critical Hölder/Besov spaces yield local and global well-posedness for the Muskat equation with surface tension and Peskin problems with nonlinear elastic tension.
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Global Existence of Weak Martingale Solutions to the Camassa-Holm Equation with Linear Multiplicative Noise
Global existence of H¹ martingale solutions to the stochastic Camassa-Holm equation is shown via viscous Galerkin approximations, tightness, and Skorokhod-Jakubowski representations.
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Invariant Measure of the Camassa-Holm Equation with Linear Multiplicative Noise
Proves almost sure continuous dependence of the solution map on initial data in H^s (s>3/2) and existence of non-unique invariant measures for the Camassa-Holm equation with linear multiplicative noise.
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Temporal decay estimates for global solutions of the Navier-Stokes equations with the Coriolis force
Global solutions to Navier-Stokes with Coriolis force decay at linearized rates, faster than heat flow, in L^p norms for p in [2, infinity] when initial data is small.
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Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
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Global well-posedness and temporal decay estimates for the viscous $\beta$-plane equations
Global smooth solutions exist for small data in the viscous β-plane equations, with decay faster than the heat equation and asymptotic behavior matching the linear kernel.
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On the Critical One Components Regularity for the $3-D$ Navier-Stokes System in $L^p_T(\dot{B}^{\frac 1 2+\frac 2 p}_{2,\infty})$ spaces
If a mild solution to 3D incompressible Navier-Stokes with v0 in Ḣ^{1/2} and Ω0 in L^{r0} (r0∈(1,2)) blows up at T*, then for any 2<p<∞ and unit vector e the integral ∫_0^{T*} ||(v(t)|e)||_{Ḃ^{1/2+2/p}_{2,∞}}^p dt diverges at T*.
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Solutions of the 3D inhomogeneous incompressible Navier-Stokes system with initial velocity in $VMO^{-1}$
Establishes local strong solutions and conditional global solutions for 3D inhomogeneous NS with data in C¹ × (L² ∩ VMO^{-1}) using density transport regularity and a new freezing-coefficient approach for momentum.
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Blow-Up Criteria and Weak--Strong Uniqueness for Compressible Fluid--Viscoelastic Shell Interactions
A Beale-Kato-Majda Lipschitz control on density and velocity gradients with strong time integrability, combined with material acceleration estimates, yields a continuation criterion and weak-strong uniqueness for the compressible fluid-viscoelastic shell system.
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Topics in Gaussian Wiener chaos expansion
These lecture notes assemble the standard Wiener-chaos toolbox — Hermite polynomials, Wick calculus, the Gaussian free field, and Φ⁴ renormalisation — for a summer-school audience.
- Nonexistence of finite-time blow-up for the equivariant harmonic map heat flow from $B^2$ to $S^2$