Communications in Mathematical Sciences

Volume 18 (2020)

Number 4

Global strong solutions to compressible Navier–Stokes system with degenerate heat conductivity and density-depending viscosity

Pages: 973 – 985

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n4.a4

Authors

Bin Huang (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, China)

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

Ying Sun (School of Mathematics Sciences, Xiamen University, Xiamen, China)

Abstract

We consider the compressible Navier–Stokes system where the viscosity depends on density and the heat conductivity is proportional to a positive power of the temperature under stress-free and thermally insulated boundary conditions. Under the same conditions on the initial data as those of the constant viscosity and heat conductivity case [Kazhikhov-Shelukhin. J. Appl. Math. Mech. 41, 1977], we obtain the existence and uniqueness of global strong solutions. Our result can be regarded as a natural generalization of Kazhikhov’s theory for the constant heat conductivity case to the degenerate and nonlinear case under stress-free and thermally insulated boundary conditions.

Keywords

compressible Navier–Stokes system, density-depending viscosity, degenerate heat conductivity, stress-free

2010 Mathematics Subject Classification

60F10, 60J75, 62P10, 92C37

Full Text (PDF format)

Received 14 March 2019

Accepted 13 January 2020

Published 28 July 2020