Time-asymptotic stability of composite wave for the one-dimensional compressible fluid of Kortwewg type

2025/02/03 by Han, Sungho, Kim, Jeongho · 1 citation
#35Q35 #76N06 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.01063

Abstract

We study the asymptotic stability of a composition of rarefaction and shock waves for the one-dimensional barotropic compressible fluid of Korteweg type, called the Navier-Stokes-Korteweg(NSK) system. Precisely, we show that the solution to the NSK system asymptotically converges to the composition of the rarefaction wave and shifted viscous-dispersive shock wave, under certain smallness assumption on the initial perturbation and strength of the waves. Our method is based on the method of a-contraction with shift developed by Kang and Vasseur \citeKV16, successfully applied to obtain contraction or stability of nonlinear waves for hyperbolic systems.

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• Asymptotic stability of composite waves of shock profile and rarefaction for the Navier-Stokes-Poisson system

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