On the Lq-Lr estimates of the Stokes semigroup in a two dimensional exterior domain Dedicated to Professor Rentaro Agemi on the occasion of his sixtieth birthday

Wakako DAN; Yoshihiro SHIBATA

doi:10.2969/jmsj/05110181

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

On the L_q-L_r estimates of the Stokes semigroup in a two dimensional exterior domain

Dedicated to Professor Rentaro Agemi on the occasion of his sixtieth birthday

Wakako DAN, Yoshihiro SHIBATA

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Keywords: Stokes semigroup, L_q-L_r estimates, boundary value problem in a two dimensional exterior domain, low frequency asymptotic behavior, local energy decay

JOURNAL FREE ACCESS

1999 Volume 51 Issue 1 Pages 181-207

DOI https://doi.org/10.2969/jmsj/05110181

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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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