Decay properties of the Stokes semigroup in exterior domains with Neumann boundary condition

Yoshihiro Shibata; Senjo Shimizu

doi:10.2969/jmsj/1180135499

Decay properties of the Stokes semigroup in exterior domains with Neumann boundary condition

Yoshihiro Shibata^*, Senjo Shimizu

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

In this paper, we obtain local energy decay estimates and L _p-L_q estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.

Original language	English
Pages (from-to)	1-34
Number of pages	34
Journal	Journal of the Mathematical Society of Japan
Volume	59
Issue number	1
DOIs	https://doi.org/10.2969/jmsj/1180135499
Publication status	Published - 2007 Jan
Externally published	Yes

Keywords

L-L estimates
Local energy decay
Neumann boundary condition
Stokes semigroup

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/1180135499

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abstract = "In this paper, we obtain local energy decay estimates and L p-Lq estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.",

keywords = "L-L estimates, Local energy decay, Neumann boundary condition, Stokes semigroup",

author = "Yoshihiro Shibata and Senjo Shimizu",

year = "2007",

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AU - Shibata, Yoshihiro

AU - Shimizu, Senjo

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N2 - In this paper, we obtain local energy decay estimates and L p-Lq estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.

AB - In this paper, we obtain local energy decay estimates and L p-Lq estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.

KW - L-L estimates

KW - Local energy decay

KW - Neumann boundary condition

KW - Stokes semigroup

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Decay properties of the Stokes semigroup in exterior domains with Neumann boundary condition

Abstract

Keywords

ASJC Scopus subject areas

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