Strong Solutions for 1D Compressible Navier-Stokes/Allen-Cahn System with Phase Variable Dependent Viscosity

2021/09/29 by Yan, Yuanxiang, Ding, Shijin, Li, Yinghua · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.14529

Abstract

This paper is concerned with a non-isentropic compressible Navier-Stokes/Allen-Cahn system with phase variable dependent viscosity η(χ)=χ^α and temperature dependent heat-conductivity κ(θ)=θ^β. We show the global existence of strong solutions under some assumptions on growth exponent α and initial data. It is worth noting that the initial data could be large if α≥0 is small, and the growth exponent β>0 can be arbitrary large.

Cited by

• Nonlinear stability of a composite wave to the Cauchy problem of 1-D full compressible Navier-Stokes-Allen-Cahn system
• Phase Transition in Non-isentropic Compressible Immiscible Two-Phase Flow with van der Waals Equation of State

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