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

Wakako Dan; Yoshihiro Shibata

doi:10.2969/jmsj/05110181

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

Wakako Dan, Yoshihiro Shibata

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

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.

Original language	English
Pages (from-to)	181-207
Number of pages	27
Journal	Journal of the Mathematical Society of Japan
Volume	51
Issue number	1
DOIs	https://doi.org/10.2969/jmsj/05110181
Publication status	Published - 1999

Keywords

L — L estimates
Stokes semigroup
boundary value problem in a two dimensional exterior domain
local energy decay
low frequency asymptotic behavior

ASJC Scopus subject areas

Mathematics(all)

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title = "On the Lq - Lr estimates of the Stokes semigroup in a two dimensional exterior domain",

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.",

keywords = "L — L estimates, Stokes semigroup, boundary value problem in a two dimensional exterior domain, local energy decay, low frequency asymptotic behavior",

author = "Wakako Dan and Yoshihiro Shibata",

year = "1999",

doi = "10.2969/jmsj/05110181",

language = "English",

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pages = "181--207",

journal = "Journal of the Mathematical Society of Japan",

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T1 - On the Lq - Lr estimates of the Stokes semigroup in a two dimensional exterior domain

AU - Dan, Wakako

AU - Shibata, Yoshihiro

PY - 1999

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N2 - 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.

AB - 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.

KW - L — L estimates

KW - Stokes semigroup

KW - boundary value problem in a two dimensional exterior domain

KW - local energy decay

KW - low frequency asymptotic behavior

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