204 citations · 802 across the 58 of their papers we have counts for
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Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system
Moon-Jin Kang, Alexis Vasseur
This paper is dedicated to the construction of a pseudo-norm, for which small shock profiles of the barotropic Navier-Stokes equation have a contraction property. This contraction…
Solutions of the 4-species quadratic reaction-diffusion system are bounded and , in any space dimension
Cristina Caputo, Thierry Goudon, Alexis Vasseur
We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation…
On Uniqueness of Solutions to Conservation Laws Verifying a Single Entropy Condition
Sam G. Krupa, Alexis F. Vasseur
For hyperbolic systems of conservation laws, uniqueness of solutions is still largely open. We aim to expand the theory of uniqueness for systems of conservation laws. One difficul…
Global weak solution to the viscous two-fluid model with finite energy
Alexis Vasseur, Huanyao Wen, Cheng Yu
In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two differe…
De Giorgi Techniques Applied to Hamilton-Jacobi Equations with Unbounded Right-Hand Side
L. F. Stokols, Alexis F. Vasseur
In this article we obtain Holder estimates for solutions to second-order Hamilton-Jacobi equations with super-quadratic growth in the gradient and unbounded source term. The estima…