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 Lp-Lq 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 Lp-Lq regularity estimate of exponentially decay type. The same problem was first treated by Kobayashi and Zajaczkowski  in the L2 framework by using the energy method; our approach is completely different from Kobayashi and Zajaczkowski .
ASJC Scopus subject areas
- Applied Mathematics