Dafermos [Arch. Rational Mech. Anal. 70 (1979), pp. 167–179] proved the weak/strong
principle for conservation laws. It states that Lipschitz solutions to conservation laws …

We prove the time-asymptotic stability of composite waves consisting of the superposition of
a viscous shock and a rarefaction for the one-dimensional compressible barotropic Navier …

We establish the time-asymptotic stability of solutions to the one-dimensional compressible
Navier-Stokes-Fourier equations, with initial data perturbed from Riemann data that forms a …

We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems
among all vanishing viscosity limits of solutions to associated Navier–Stokes systems. To …

We consider the so-called Naiver-Stokes-Korteweg (NSK) equations for the dynamics of
compressible barotropic viscous fluids with internal capillarity. We handle the time …

This paper is dedicated to the construction of a pseudo-norm for which small shockprofiles of
the barotropic Navier–Stokes equations have a contraction property. This contraction …

We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor
angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is …

Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a
convex entropy. We consider the family of small BV functions which are global solutions of …

We consider a L 2-contraction (a L 2-type stability) of large viscous shock waves for the multi-
dimensional scalar viscous conservation laws, up to a suitable shift by using the relative …

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 …