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

Wakako DAN; Yoshihiro SHIBATA

doi:10.2969/jmsj/05110181

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January, 1999 On the

L_{q}-L_{r}

estimates of the Stokes semigroup in a two dimensional exterior domain

Wakako DAN, Yoshihiro SHIBATA

J. Math. Soc. Japan 51(1): 181-207 (January, 1999). DOI: 10.2969/jmsj/05110181

Abstract

We proved $L_{q}-L_{r}$ 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.

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Wakako DAN. Yoshihiro SHIBATA. "On the $L_{q}-L_{r}$ estimates of the Stokes semigroup in a two dimensional exterior domain." J. Math. Soc. Japan 51 (1) 181 - 207, January, 1999. https://doi.org/10.2969/jmsj/05110181

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Published: January, 1999

First available in Project Euclid: 10 June 2008

zbMATH: 0924.35094

MathSciNet: MR1661048

Digital Object Identifier: 10.2969/jmsj/05110181

Subjects:

Primary: 35Q30

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

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J. Math. Soc. Japan

Vol.51 • No. 1 • January, 1999

Mathematical Society of Japan

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Wakako DAN, Yoshihiro SHIBATA "On the

L_{q}-L_{r}

estimates of the Stokes semigroup in a two dimensional exterior domain," Journal of the Mathematical Society of Japan, J. Math. Soc. Japan 51(1), 181-207, (January, 1999)

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