Decently regular steady solutions to the compressible NSAC system

Šimon Axman

DOI: http://dx.doi.org/10.12775/TMNA.2016.042

Abstract


We aim at proving existence of weak solutions to the stationary
compressible Navier-Stokes system coupled with the Allen-Cahn
equation - NSAC system. 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 $\gamma$ \hbox{$ (p \sim
\varrho^\gamma$)}. As a corollary we obtain weak solutions for a
less restrictive case losing pointwise boundedness of the density.

Keywords


Navier--Stokes--Allen--Cahn equations; steady compressible flow; existence and regularity of the solutions

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