On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds-Reference-Cited by-同舟云学术

On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds

Published:2008-12-30 Issue:6 Volume:361 Page:3125-3157
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Mitrea Marius,Monniaux Sylvie

Abstract

We study the analyticity of the semigroup generated by the Stokes operator equipped with Neumann-type boundary conditions on L p L^p spaces in Lipschitz domains. Our strategy is to regularize this operator by considering the Hodge Laplacian, which has the additional property that it commutes with the Leray projection.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2009-361-06/S0002-9947-08-04827-7/S0002-9947-08-04827-7.pdf

Reference27 articles.

1. On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems;Agmon, Shmuel;Comm. Pure Appl. Math.,1962

2. Extrapolation of Carleson measures and the analyticity of Kato’s square-root operators;Auscher, Pascal;Acta Math.,2001

3. T.Akiyama, H.Kasai, Y.Shibata and M.Tsutsumi, The 𝐿^{𝑝} approach to the Laplace system with some boundary conditions and applying to the parabolic system, unpublished lecture notes, 1999.

4. On a resolvent estimate of a system of Laplace operators with perfect wall condition;Akiyama, T.;Funkcial. Ekvac.,2004

5. Exact controllability for the magnetohydrodynamic equations;Barbu, Viorel;Comm. Pure Appl. Math.,2003

Cited by 35 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains;Mathematische Annalen;2024-08-03

2. The Stokes operator in two-dimensional bounded Lipschitz domains;Journal of Differential Equations;2022-12

3. $$L^p$$-theory for the exterior Stokes problem with Navier’s type slip-without-friction boundary conditions;Zeitschrift für angewandte Mathematik und Physik;2022-04-05

4. Existence in critical spaces for the magnetohydrodynamical system in 3D bounded Lipschitz domains;Journal of Elliptic and Parabolic Equations;2021-08-29

5. Stokes and Navier-Stokes equations subject to partial slip on uniform C2,1-domains in L-spaces;Journal of Differential Equations;2021-05