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
收藏
页码：203 / 226
页数：24
相关论文
共 33 条
[1]  
AL BABA H., 2015, THESIS
[2]  
Al Baba H, 2017, J EVOL EQU, V17, P641, DOI 10.1007/s00028-016-0331-9
[3]   Semi-Group Theory for the Stokes Operator with Navier-Type Boundary Conditions on L p -Spaces [J].
Al Baba, Hind ;
Amrouche, Cherif ;
Escobedo, Miguel .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 223 (02) :881-940
[4]   Analyticity of the semi-group generated by the Stokes operator with Navier-type boundary conditions on Lp-spaces [J].
Al Baba, Hind ;
Amrouche, Cherif ;
Escobedo, Miguel .
RECENT ADVANCES IN PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 666 :23-40
[5]   Effect of rugosity on a flow governed by stationary navier-stokes equations [J].
Amirat, Y ;
Bresch, D ;
Lemoine, J ;
Simon, J .
QUARTERLY OF APPLIED MATHEMATICS, 2001, 59 (04) :769-785
[6]  
AMROUCHE C., VERY WEAK SOLUTIONS
[7]   Lp-THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS [J].
Amrouche, Cherif ;
Seloula, Nour El Houda .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2013, 23 (01) :37-92
[8]   ON THE STOKES EQUATIONS WITH THE NAVIER-TYPE BOUNDARY CONDITIONS [J].
Amrouche, Cherif ;
Seloula, Nour El Houda .
DIFFERENTIAL EQUATIONS & APPLICATIONS, 2011, 3 (04) :581-607
[9]  
[Anonymous], 2011, J. Math. Sci.
[10]   On viscosity-continuous solutions of the Euler and Navier-Stokes equations with a Navier-type boundary condition [J].
Bellout, Hamid ;
Neustupa, Jiri ;
Penel, Patrick .
COMPTES RENDUS MATHEMATIQUE, 2009, 347 (19-20) :1141-1146
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