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ON LOCAL ENERGY DECAY ESTIMATE OF THE OSEEN SEMIGROUP IN TWO DIMENSIONS AND ITS APPLICATION

Part of: Incompressible viscous fluids Partial differential equations

Published online by Cambridge University Press:  01 July 2019

Yasunori Maekawa
Yasunori Maekawa*
Affiliation:
Department of Mathematics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto606-8502, Japan (maekawa@math.kyoto-u.ac.jp)
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Abstract

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We study the temporal decay estimate of the Oseen semigroup in a two-dimensional exterior domain. We establish the local energy decay estimate with a suitable dependence on the small translation speed, which is a significant improvement of Hishida’s result in 2016. As an application, we prove the $L^{q}$-$L^{r}$ estimates of the Oseen semigroup uniformly in the small translation speed.

Keywords

Oseen semigrouptwo-dimensional flows past an obstaclelocal energy decayresolvent analysis

MSC classification

Primary: 76D07: Stokes and related (Oseen, etc.) flows
Secondary: 35B35: Stability
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 3 , May 2021 , pp. 859 - 891
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Copyright
© Cambridge University Press 2019

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