Vanishing viscosity in the Navier–Stokes equations of compressible heat-conducting flows with the spherical symmetry

Abstract

In this paper, we study the limit process as the bulk viscosity goes to zero for global weak solutions to the Navier–Stokes equations of compressible heat-conducting flows with density-dependent viscosity coefficient and general heat conductivity. We prove that the limit of the global solutions is a weak solution of the corresponding system with zero bulk viscosity.

Keywords:

• Navier–Stokes equations
• compressible heat-conducting flows
• spherically symmetric
• density-dependent viscosity coefficient
• vanishing viscosity

2010 Mathematics Subject Classifications:

• 76M45
• 76N10
• 35L65

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

W. Song is partially supported by the National Natural Sciences Foundation of China under the grants 11561076 and 11601423.