Decently regular steady solutions to the compressible NSAC system - Axman, Šimon (Topological Methods in Nonlinear Analysis, 2016)
We aim at proving existence of weak solutions to the stationarycompressible Navier-Stokes system coupled with the Allen-Cahnequation - NSAC system. The model is studied in a bounded threedimensional domain with slip boundary conditions for the momentumequations and the Neumann condition for the Allen-Cahn model. Themain result establishes existence of weak solutions with boundeddensities. The construction is possible assuming sufficientlylarge value of the heat capacity ratio $γ$ \hbox{$ (p \simρ^γ$)}. As a corollary we obtain weak solutions for aless restrictive case losing pointwise boundedness of the density.