10 papers
Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations
Moon-Jin Kang, Alexis F. Vasseur, Yi Wang
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 Navie…
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…
Global well-posedness of large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model
Kyudong Choi, Moon-Jin Kang, Alexis Vasseur
We consider a one-dimensional system arising from a chemotaxis model in tumour angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. This hyperboli…
Propagation of the mono-kinetic solution in the Cucker-Smale-type kinetic equations
Moon-Jin Kang, Jeongho Kim
In this paper, we study the propagation of the mono-kinetic distribution in the Cucker-Smale-type kinetic equations. More precisely, if the initial distribution is a Dirac mass for…
Global smooth solutions for 1D barotropic Navier-Stokes equations with a large class of degenerate viscosities
Moon-Jin Kang, Alexis Vasseur
We prove the global existence and uniqueness of smooth solutions to the one-dimensional barotropic Navier-Stokes system with degenerate viscosity . We establish that the…
Inviscid limit to the shock waves for the fractal Burgers equation
Sona Akopian, Moon-Jin Kang, Alexis Vasseur
We show the vanishing viscosity limit to entropy shocks for the fractal Burgers equation in one space dimension. More precisely, we quantify the rate of convergence of the inviscid…