$L_p$–$L_q$ maximal regularity of the Neumann problem for the Stokes equations in a bounded domain

Shibata, Yoshihiro; Shimizu, Senjo

doi:10.2969/aspm/04710349

VOL. 47.1 | 2007 $L_p$–$L_q$ maximal regularity of the Neumann problem for the Stokes equations in a bounded domain

Chapter Author(s) Yoshihiro Shibata, Senjo Shimizu

Editor(s) Hideo Kozono, Takayoshi Ogawa, Kazunaga Tanaka, Yoshio Tsutsumi, Eiji Yanagida

Adv. Stud. Pure Math., 2007: 349-362 (2007) DOI: 10.2969/aspm/04710349

Abstract

We consider the Neumann problem for the Stokes equations with non-homogeneous boundary and divergence conditions in a bounded domain. We obtain a global in time $L_p$-$L_q$ maximal regularity theorem with exponential stability. To prove the $L_p$-$L_q$ maximal regularity, we use the Weis operator valued Fourier multiplier theorem.