ON THE STOKES EQUATIONS WITH THE NAVIER-TYPE BOUNDARY CONDITIONS

被引：34
|
作者：
Amrouche, Cherif [1 ]
Seloula, Nour El Houda [2 ,3 ,4 ]
机构：
[1] Univ Pau & Pays Adour, LMA, Ave Univ, F-64013 Pau, France
[2] EPI Concha, INRIA Bordeaux Sud Ouest, F-64013 Pau, France
[3] Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France
[4] INRIA Bordeaux Sud Ouest, EPI MC2, Cours Liberat 351, F-33405 Talence, France
来源：
DIFFERENTIAL EQUATIONS & APPLICATIONS | 2011年 / 3卷 / 04期
关键词：
vector potentials; L-p-theory; Navier boundary conditions; Stokes equations; inf-sup condition; Sobolev inequality;
D O I：
10.7153/dea-03-36
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In a possibly multiply-connected three dimensional bounded domain, we prove in the L-p theory the existence and uniqueness of vector potentials, associated with a divergence-free function and satisfying non homogeneous boundary conditions. Furthermore, we consider the stationary Stokes equations with nonstandard boundary conditions of the form u center dot n = g and curlu x n = h x n on the boundary Gamma. We prove the existence and uniqueness of weak, strong and very weak solutions. Our proofs are mainly based on In f -Sup conditions.
引用
收藏
页码：581 / 607
页数：27
相关论文
共 50 条
  • [1] The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions
    Neustupa, Jiri
    Al Baba, Hind
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 463 (01) : 222 - 234
  • [2] On L3-stability of strong solutions of the Navier-Stokes equations with the Navier-type boundary conditions
    Kucera, Petr
    Neustupa, Jiri
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 405 (02) : 731 - 737
  • [3] ON A ν-CONTINUOUS FAMILY OF STRONG SOLUTIONS TO THE EULER OR NAVIER-STOKES EQUATIONS WITH THE NAVIER-TYPE BOUNDARY CONDITION
    Bellout, Hamid
    Neustupa, Jiri
    Penel, Patrick
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (04) : 1353 - 1373
  • [4] On viscosity-continuous solutions of the Euler and Navier-Stokes equations with a Navier-type boundary condition
    Bellout, Hamid
    Neustupa, Jiri
    Penel, Patrick
    [J]. COMPTES RENDUS MATHEMATIQUE, 2009, 347 (19-20) : 1141 - 1146
  • [5] L2-Decay of Solutions to the Navier-Stokes System with Navier-Type Boundary Conditions
    Al Baba, Hind
    Jazar, Mustapha
    [J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2021, 23 (03)
  • [6] VECTOR POTENTIALS WITH MIXED BOUNDARY CONDITIONS. APPLICATION TO THE STOKES PROBLEM WITH PRESSURE AND NAVIER-TYPE BOUNDARY CONDITIONS
    Amrouche, Cherif
    Boussetouan, Imane
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (02) : 1745 - 1784
  • [7] STOKES AND NAVIER-STOKES PROBLEMS WITH NAVIER-TYPE BOUNDARY CONDITION IN LP-SPACES
    Al Baba, Hind
    Amrouche, Cherif
    [J]. DIFFERENTIAL EQUATIONS & APPLICATIONS, 2019, 11 (02): : 203 - 226
  • [8] Stokes and Navier-Stokes equations with Navier boundary conditions
    Acevedo Tapia, P.
    Amrouche, C.
    Conca, C.
    Ghosh, A.
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 285 : 258 - 320
  • [9] Semi-Group Theory for the Stokes Operator with Navier-Type Boundary Conditions on L p -Spaces
    Al Baba, Hind
    Amrouche, Cherif
    Escobedo, Miguel
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 223 (02) : 881 - 940
  • [10] The compressible Navier–Stokes equations with slip boundary conditions of friction type
    Šárka Nečasová
    Justyna Ogorzaly
    Jan Scherz
    [J]. Zeitschrift für angewandte Mathematik und Physik, 2023, 74
12345