## Advanced Studies in Pure Mathematics

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

#### 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.

#### Article information

Dates
Revised: 24 February 2006
First available in Project Euclid: 16 December 2018

https://projecteuclid.org/ euclid.aspm/1545000603

Digital Object Identifier
doi:10.2969/aspm/04710349

Mathematical Reviews number (MathSciNet)
MR2387244

Zentralblatt MATH identifier
1141.35344

#### Citation

Shibata, Yoshihiro; Shimizu, Senjo. $L_p$–$L_q$ maximal regularity of the Neumann problem for the Stokes equations in a bounded domain. Asymptotic Analysis and Singularities — Hyperbolic and dispersive PDEs and fluid mechanics, 349--362, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04710349. https://projecteuclid.org/euclid.aspm/1545000603