The limit to rarefaction wave with vacuum for 1D compressible fluids with temperature-dependent viscosities

2013/07/12 by Mingjie Li, Teng Wang, Li, Mingjie +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1307.3382

openalex publication_date 2013/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the zero dissipation limit of the one-dimensional full compressible Navier-Stokes(CNS) equations with temperature-dependent viscosity and heat-conduction coefficient. It is proved that given a rarefaction wave with one-side vacuum state to the full compressible Euler equations, we can construct a sequence of solutions to the full CNS equations which converge to the above rarefaction wave with vacuum as the viscosity and the heat conduction coefficient tend to zero. Moreover, the uniform convergence rate is obtained. The main difficulty in our proof lies in the degeneracies of the density, the temperature and the temperature-dependent viscosities at the vacuum region in the zero dissipation limit.

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