Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations

MJ Kang, AF Vasseur, Y Wang - Advances in Mathematics, 2023‏ - Elsevier
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 …

Time-asymptotic stability of generic Riemann solutions for compressible Navier-Stokes-Fourier equations

MJ Kang, A Vasseur, Y Wang - arxiv preprint arxiv:2306.05604, 2023‏ - arxiv.org
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 …

Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier–Stokes systems

MJ Kang, AF Vasseur - Inventiones mathematicae, 2021‏ - Springer
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 …

Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system

MJ Kang, AF Vasseur - Journal of the European Mathematical Society, 2020‏ - ems.press
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 …

decay for large perturbations of viscous shocks for multi-D Burgers equation

MJ Kang, HS Oh - arxiv preprint arxiv:2403.08445, 2024‏ - arxiv.org
We consider a planar viscous shock of moderate strength for a scalar viscous conservation
law in multi-D. We consider a strictly convex flux, as a small perturbation of the Burgers flux …

Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model

K Choi, MJ Kang, YS Kwon… - Mathematical Models and …, 2020‏ - World Scientific
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 …

Criteria on contractions for entropic discontinuities of systems of conservation laws

MJ Kang, AF Vasseur - Archive for Rational Mechanics and Analysis, 2016‏ - Springer
We study the contraction properties (up to shift) for admissible Rankine–Hugoniot
discontinuities of n * nn× n systems of conservation laws endowed with a convex entropy …

Long-time behavior towards viscous-dispersive shock for Navier-Stokes equations of Korteweg type

S Han, MJ Kang, J Kim, H Lee - Journal of Differential Equations, 2025‏ - Elsevier
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 …

Nonlinear stability of planar viscous shock wave to three-dimensional compressible Navier–Stokes equations

T Wang, Y Wang - Journal of the European Mathematical Society, 2024‏ - ems.press
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 …

L2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

MJ Kang, AF Vasseur, Y Wang - Journal of Differential Equations, 2019‏ - Elsevier
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 …