Communications in Mathematical Sciences

Volume 19 (2021)

Number 5

Stability of degenerate stationary solution to the outflow problem for full Navier–Stokes equations

Pages: 1233 – 1246

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n5.a3

Authors

Yazhou Chen (Department of Mathematics, College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, China)

Hakho Hong (Institute of Mathematics, State Academy of Sciences, Pyongyang, D.P.R. Korea)

Xiaoding Shi (Department of Mathematics, College of Mathematics and Physics, Beijing, China; and University of Chemical Technology, Beijing, China)

Abstract

This paper is concerned with large-time behavior of solutions to the outflow problem of full compressible Navier–Stokes equations in the half line. This is one out of the series of papers by the authors on the stability of nonlinear waves to the outflow problem. We show the time-asymptotic stability of degenerate (transonic) stationary solution for the general gas including ideal polytropic gas. The proof is based on delicate energy estimates.

Keywords

compressible, Navier–Stokes equations, outflow problem, stationary solution, stability

2010 Mathematics Subject Classification

35B35, 35L65, 35Q30, 74J40, 76D33

Received 16 May 2020

Accepted 24 December 2020

Published 7 July 2021