On a maximal Lp–LqLp–Lq approach to the compressible viscous fluid flow with slip boundary condition

In this paper, we prove a local in time unique existence theorem for the compressible viscous fluids in the general domain with slip boundary condition. For the purpose, we use the contraction mapping principle based on the maximal Lp–LqLp–Lq regularity by means of the Weis operator valued Fourier multiplier theorem for the corresponding time dependent problem. To obtain the maximal Lp–LqLp–Lq regularity, we prove the sectorial RR-boundedness of the solution operator to the generalized Stokes equations.