Decently regular steady solutions to the compressible NSAC system

2015/01/25 by Axmann, Šimon, Mucha, Piotr B. · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.06150

Abstract

We aim at proving existence of weak solutions to the stationary compressible Navier-Stokes system coupled with the Allen-Cahn equation. The model is studied in a bounded three dimensional domain with slip boundary conditions for the momentum equations and the Neumann condition for the Allen-Cahn model. The main result establishes existence of weak solutions with bounded densities. The construction is possible assuming sufficiently large value of the heat capacity ratio γ (p ∼ ρ^γ). As a corollary we obtain weak solutions for a less restrictive case losing point-wise boundedness of the density.

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• Nonlinear stability of a composite wave to the Cauchy problem of 1-D full compressible Navier-Stokes-Allen-Cahn system

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