Some a priori estimate related to the well-posedness for the barotropic compressible Navier-Stokes system (Harmonic Analysis and Nonlinear Partial Differential Equations)

"Harmonic Analysis and Nonlinear Partial Differential Equations". July 4～6, 2016. edited by Hideo Kubo and Hideo Takaoka. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We consider some global a priori estimate related to the well-posedness for the barotropic compressible Navier-Stokes system. We employ the Fourier-Herz spaces instead of the standard Besov spaces, and show a global in time a priori bound of the solutions for the initial data in the Lq-type regularity framework