Local strong solution for the viscous compressible and heat-conductive fluids with vacuum in 2D space

2015/08/16 by Zhilei Liang, Liang, Zhilei
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1508.03791

openalex publication_date 2015/08/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper considers the Cauchy problem of equations for the viscous compressible and heat-conductive fluids in the two-dimensional(2D) space. We establish the local existence theory of unique strong solution under some initial layer compatibility conditions. The initial data can be arbitrarily large, the initial density is allowed to vanish in any set and the far field state is assumed to be vacuum.

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