Long-time behavior toward composite wave of shocks for 3D barotropic navier-stokes system
Analysis of PDEs
2024-06-18 v1
Abstract
We consider the barotropic Navier-Stokes system in three space dimensions with periodic boundary condition in the transversal direction. We show the long-time behavior of the 3D barotropic Navier-Stokes flow perturbed from a composition of two shock waves with suitably small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in space, towards a composition of two planar viscous shock waves as time goes to infinity, up to dynamical shifts. This is the first result on time-asymptotic stability of composite wave of two shocks for multi-D Navier-Stokes system. The main part of proof is based on the method of a-contraction with shifts.
Keywords
Cite
@article{arxiv.2406.11215,
title = {Long-time behavior toward composite wave of shocks for 3D barotropic navier-stokes system},
author = {Moon-Jin Kang and Hobin Lee},
journal= {arXiv preprint arXiv:2406.11215},
year = {2024}
}