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

TL;DR

This paper proves the local existence and uniqueness of strong solutions for 2D viscous compressible heat-conductive fluids with vacuum, allowing large initial data and initial density vanishing in regions.

Contribution

It establishes the local strong solution existence for 2D viscous compressible heat-conductive fluids with vacuum, even with large initial data and density vanishing regions.

Findings

Existence of unique strong solutions under initial layer conditions

Initial density can vanish in arbitrary regions

Solutions exist despite large initial data

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.