STOKES AND NAVIER-STOKES PROBLEMS WITH NAVIER-TYPE BOUNDARY CONDITION IN LP-SPACES

被引：4

作者：

Al Baba, Hind ^{[1
,2
]}

Amrouche, Cherif ^{[2
]}

机构：

[1] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567 1, Czech Republic

[2] Univ Pau & Pays Adour, UMR CNRS 5142, Lab Math & Leurs Applicat, F-64013 Pau, France

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2019年 / 11卷 / 02期

关键词：

Stokes and Navier-Stokes Problem; Navier-type boundary conditions; EQUATIONS; REGULARITY; FLOW;

D O I：

10.7153/dea-2019-11-08

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the semigroup theory for the Stokes equation with Navier type boundary conditions developed in [2, 3], we first prove the maximal L-p - L-q regularity for the strong, weak and very weak solutions of the inhomogeneous Stokes problem with Navier-type boundary conditions in a bounded domain Omega, not necessarily simply connected. We also prove the existence of a unique local in time classical solution to the Navier Stokes problem with Navier-type boundary conditions and show that it is global in time for small initial data.

引用

页码：203 / 226

页数：24

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