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 study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit
solution of the three‐dimensional incompressible Euler equations. The flow is axi‐symmetric …

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 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 …

As a continuum model for compressible fluid flows, Howard Brenner proposed the so-called
Brenner-Navier-Stokes-Fourier (BNSF) system that improves some flaws of the Navier …