## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Asymptotic Analysis and Singularities — Hyperbolic and dispersive PDEs and fluid mechanics, H. Kozono, T. Ogawa, K. Tanaka, Y. Tsutsumi and E. Yanagida, eds. (Tokyo: Mathematical Society of Japan, 2007), 349 - 362

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

Yoshihiro Shibata and Senjo Shimizu

#### 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**

Received: 31 October 2005

Revised: 24 February 2006

First available in Project Euclid:
16 December 2018

**Permanent link to this document**

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