204 citations · 802 across the 58 of their papers we have counts for
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Sharp a-contraction estimates for small extremal shocks
William Golding, Sam Krupa, Alexis Vasseur
In this paper, we study the -contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected t…
Well-posedness of the Riemann problem with two shocks for the isentropic Euler system in a class of vanishing physical viscosity limits
Moon-Jin Kang, Alexis Vasseur
We consider the Riemann problem composed of two shocks for the 1D Euler system. We show that the Riemann solution with two shocks is stable and unique in the class of weak inviscid…
Uniqueness and weak-BV stability for conservation laws
Geng Chen, Sam G. Krupa, Alexis F. Vasseur
Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small functions which are global solutions of…
Second derivatives estimate of suitable solutions to the 3D Navier-Stokes equations
Alexis Vasseur, Jincheng Yang
We study the second spatial derivatives of suitable weak solutions to the incompressible Navier-Stokes equations in dimension three. We show that it is locally fo…
Instability for Axisymmetric Blow-up Solutions to Incompressible Euler Equations
Laurent Lafleche, Alexis F. Vasseur, Misha Vishik
It is still not known whether a solution to the incompressible Euler equation, endowed with a smooth initial value, can blow-up in finite time. In [{\em Comm. Math. Phys.}, 378:557…
On the Exponential decay for Compressible Navier-Stokes-Korteweg equations with a Drag Term
Didier Bresch, Marguerite Gisclon, Ingrid Lacroix-Violet +1
In this paper, we consider global weak solutions to com-pressible Navier-Stokes-Korteweg equations with density dependent viscosities , in a periodic domain , with…