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 Lq-Lq regularity by means of the Weis operator valued Fourier multiplier theorem for the corresponding time dependent problem. To obtain the maximal Lp-Lq regularity, we prove the sectorial R-boundedness of the solution operator to the generalized Stokes equations.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2014|
ASJC Scopus subject areas