Communications in Mathematical Sciences

Volume 18 (2020)

Number 7

Nonlinear stability of composite waves for one-dimensional compressible Navier–Stokes equations for a reacting mixture

Pages: 1977 – 2004

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n7.a7

Authors

Zefu Feng (School of Mathematical Sciences, South China University of Technology, Guangzhou, China)

Mei Zhang (School of Mathematics, South China University of Technology, Guangzhou, China)

Changjiang Zhu (School of Mathematics, South China University of Technology, Guangzhou, China)

Abstract

In this paper, we study the long-time behavior of the solutions for the initial-boundary value problem to a one-dimensional Navier–Stokes equations for a reacting mixture in a half line $\mathbb{R}_{+} := (0, \infty)$. We give the asymptotic stability of not only stationary solution for the impermeability problem but also the composite waves consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem of Navier–Stokes equations for a reacting mixture under some smallness conditions. The proofs are based on basic energy method.

Keywords

compressible Navier–Stokes equations, reacting mixture, composite waves, nonlinear stability

2010 Mathematics Subject Classification

35B40, 35Q35, 76N10

Full Text (PDF format)

The author Zhu was supported by the National Natural Science Foundation of China #11771150, 11831003, 11926346 and Guangdong Basic and Applied Basic Research Foundation #2020B1515310015. Zhang was supported by the National Natural Science Foundation of China #11701185, 11126072 and The Fundamental Research Funds for the Central Universities (No. 2011ZM0085). Feng was supported by the Fundamental Research Funds for the Central Universities (No. D2172260) and Grant from SCUT (No. D6182820).

Received 15 August 2019

Accepted 10 May 2020

Published 11 December 2020