Open Access
Translator Disclaimer
July, 2007 The Stokes and Navier-Stokes equations in an aperture domain
Takayuki KUBO
J. Math. Soc. Japan 59(3): 837-859 (July, 2007). DOI: 10.2969/jmsj/05930837

Abstract

We consider the nonstationary Stokes and Navier-Stokes equations in an aperture domain Ω R n , n 2 . For this purpose, we prove L p - L q type estimate of the Stokes semigroup in the aperture domain. Our proof is based on the local energy decay estimate obtained by investigation of the asymptotic behavior of the resolvent of the Stokes operator near the origin. We apply them to the Navier-Stokes initial value problem in the aperture domain. As a result, we can prove the global existence of a unique solution to the Navier-Stokes problem with the vanishing flux condition and some decay properties as t , when the initial velocity is sufficiently small in the L n space. Moreover we can prove the time-local existence of a unique solution to the Navier-Stokes problem with the non-trivial flux condition.

Citation

Download Citation

Takayuki KUBO. "The Stokes and Navier-Stokes equations in an aperture domain." J. Math. Soc. Japan 59 (3) 837 - 859, July, 2007. https://doi.org/10.2969/jmsj/05930837

Information

Published: July, 2007
First available in Project Euclid: 5 October 2007

zbMATH: 1171.35097
MathSciNet: MR2344831
Digital Object Identifier: 10.2969/jmsj/05930837

Subjects:
Primary: 35J55
Secondary: 76D07

Keywords: $L^p$-$L^q$ estimate , aperture domain , Navier-Stokes equations , Stokes equations

Rights: Copyright © 2007 Mathematical Society of Japan

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.59 • No. 3 • July, 2007
Back to Top