Communications in Mathematical Sciences
Volume 20 (2022)
Zero dissipation limit problem of 1-D Navier–Stokes equations
Pages: 1305 – 1329
The zero dissipation limit problem of the Navier–Stokes equations with zero viscosity in the case of the superposition of two rarefaction waves and a contact discontinuity is considered in this paper. It is proved that when the heat conductivity coefficient tends to zero, there exists a unique global solution of the compressible Navier–Stokes equations which converges uniformly to the Riemann solution of the corresponding Euler equations away from the initial time and the contact discontinuity. In addition, the uniform convergence rate in terms of the heat conductivity coefficient is obtained. This result is proved by a combination of the energy method from [F.M. Huang, Y. Wang, and T. Yang, Kinet. Relat. Models, 3:685–728, 2010] and [S.X. Ma, J. Math. Anal. Appl., 387:1033–1043, 2012].
Navier–Stokes equations, composite wave, inviscid limit
2010 Mathematics Subject Classification
35L65, 35Q30, 76N10, 76N15
This paper’s subject classification codes were emended on 1 June 2022.
The first author is partially supported by the National Natural Science Foundation of China (Nos. 11771155, 11771297), and by the Natural Science Foundation of Guangdong Province (No. 2021A1515010249).
Received 23 February 2021
Accepted 30 November 2021
Published 26 May 2022