FROM STRONG TO VERY WEAK SOLUTIONS TO THE STOKES SYSTEM WITH NAVIER BOUNDARY CONDITIONS IN THE HALF-SPACE

被引：5

作者：

Amrouche, Cherif ^{[1
]}

Necasova, Sarka ^{[2
]}

Raudin, Yves ^{[1
]}

机构：

[1] Univ Pau & Pays Adour, Lab Math Appl, CNRS, IPRA,UMR 5142, F-64000 Pau, France

[2] Acad Sci Czech Republic, Math Inst, CR-11567 Prague 1, Czech Republic

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2009年 / 41卷 / 05期

关键词：

Stokes problem; half-space; weighted Sobolev spaces; WEIGHTED SOBOLEV SPACES; BIHARMONIC PROBLEM; REGULARITY; ROUGHNESS; EQUATIONS; DOMAINS; R(N); FLOW;

D O I：

10.1137/090749207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Stokes problem with slip-type boundary conditions in the half-space R-+(n), with n >= 2. The weighted Sobolev spaces yield the functional framework. We first study generalized and strong solutions and then the case with very low regularity of data on the boundary. We apply the method of decomposition introduced in our previous work [J. Differential Equations, 244 (2008), pp. 887-915] where it is necessary to solve particular problems for harmonic and biharmonic operators with very weak data. We also envisage a wide class of behaviors at infinity for data and solutions.

引用

页码：1792 / 1815

页数：24

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