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

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 prove the nonlinear stability of the planar viscous shock up to a time-dependent shift for
the three-dimensional (3D) compressible Navier–Stokes equations under the generic …

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 the hydrodynamic limit of a collisionless and non-diffusive kinetic equation
under strong local alignment regime. The local alignment is first considered by Karper …

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 …

We are concerned with the large-time behavior of the solution to one-dimensional (1D) cubic
non-convex scalar viscous conservation laws. Due to the inflection point of the cubic non …