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We aim at proving existence of weak solutions to the stationary compressibleNavier-Stokes system coupled with the Allen-Cahn equation. The model is studiedin a bounded three dimensional domain with slip boundary conditions for themomentum equations and the Neumann condition for the Allen-Cahn model. The mainresult establishes existence of weak solutions with bounded densities. Theconstruction is possible assuming sufficiently large value of the heat capacityratio $\gamma$ ($p \sim \rho^\gamma$). As a corollary we obtain weak solutionsfor a less restrictive case losing point-wise boundedness of the density.

Decently regular steady solutions to the compressible NSAC system