Stability of large amplitude viscous shock wave for 1-D isentropic Navier–Stokes system in the half space

In this paper, the asymptotic-time behavior of solutions to an initial boundary value problem in the half space for 1‑D isentropic Navier–Stokes system is investigated. It is shown that the viscous shock wave is stable for an impermeable wall problem where the velocity is zero on the boundary provided that the shock wave is initially far away from the boundary. Moreover, the strength of the shock wave could be arbitrarily large. This work essentially improves the result of [A. Matsumura and M. Mei, Arch. Ration. Mech. Anal., 146(1):1–22, 1999], where the strength of the shock wave is sufficiently small.

Keywords

impermeable wall problem, large amplitude shock, asymptotic stability

2010 Mathematics Subject Classification

35Q30, 76N10

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Received 30 March 2021

Received revised 29 December 2021

Accepted 7 January 2022

Published 26 May 2022