On the global well-posedness for the compressible Navier-Stokes equations with slip boundary condition

In this paper, we prove a global in time unique existence theorem for the compressible viscous fluids in a bounded domain with slip boundary condition in the maximal L_p-L_q regularity class with 2<p<∞ and N<q<∞ under the assumption that initial data are small enough and orthogonal to rigid motions if domain is rotationally symmetric. To prove the global well-posedness, we use the prolongation argument based on the maximal L_p-L_q regularity estimate of exponentially decay type. The same problem was first treated by Kobayashi and Zajaczkowski [5] in the L₂ framework by using the energy method; our approach is completely different from Kobayashi and Zajaczkowski [5].