Viscous limit to contact discontinuity for the 1-D compressible Navier-Stokes equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:387

Article

Ma, Shixiang^1,2 

[1] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China

关键词: Compressible Navier-Stokes equations;    Compressible Euler system;    Zero dissipation limit;    Contact discontinuity;   

DOI  :  10.1016/j.jmaa.2011.10.010

来源: Elsevier

【 摘 要 】

In this paper, we study the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations. We prove that if the solution of the inviscid Euler equations is piecewise constants with a contact discontinuity, then there exist smooth solutions to the Navier-Stokes equations which converge to the inviscid solution away from the contact discontinuity at a rate of kappa(3/4) as the heat-conductivity coefficient kappa tends to zero, provided that the viscosity mu is higher order than the heat-conductivity kappa or the same order as kappa. Here we have no need to restrict the strength of the contact discontinuity to be small. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free