Journal of the Mathematical Society of Japan

On the Lq-Lr estimates of the Stokes semigroup in a two dimensional exterior domain

Wakako DAN and Yoshihiro SHIBATA

Full-text: Open access

Abstract

We proved Lq-Lr type estimates of the Stokes semigroup in a two dimensional exterior 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.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 181-207.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108357

Digital Object Identifier
doi:10.2969/jmsj/05110181

Mathematical Reviews number (MathSciNet)
MR1661048

Zentralblatt MATH identifier
0924.35094

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]

Keywords
Stokes semigroup $L_{q}-L_{r}$ estimates boundary value problem in a two dimensional exterior domain low frequency asymptotic behavior local energy decay

Citation

DAN, Wakako; SHIBATA, Yoshihiro. On the $L_{q}-L_{r}$ estimates of the Stokes semigroup in a two dimensional exterior domain. J. Math. Soc. Japan 51 (1999), no. 1, 181--207. doi:10.2969/jmsj/05110181. https://projecteuclid.org/euclid.jmsj/1213108357


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