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

Yoshihiro Shibata; Senjo Shimizu

doi:10.2969/jmsj/1180135499

Journal of the Mathematical Society of Japan

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

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

Yoshihiro Shibata, Senjo Shimizu

著者情報

キーワード: L_p-L_q estimates, local energy decay, Stokes semigroup, Neumann boundary condition

ジャーナルフリー

2007 年 59 巻 1 号 p. 1-34

DOI https://doi.org/10.2969/jmsj/1180135499

詳細

抄録

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.