Stokes and Navier-Stokes equations with Navier boundary conditions

We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Ω⊂R3 of class C1,1. We prove the existence and uniqueness of weak and strong solutions in W1,p(Ω) and W2,p(Ω) for all 1<p<∞, considering minimal regularity on the frict...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 285; pp. 258 - 320
Main Authors Acevedo Tapia, P., Amrouche, C., Conca, C., Ghosh, A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.06.2021
Subjects
[formula omitted]-regularity
Inf-sup condition
Navier-Stokes equations
Nonhomogeneous Navier boundary conditions
Stokes equations
Weak solution
Weak solution
Lp-regularity
Inf-sup condition
Nonhomogeneous Navier boundary conditions
Stokes equations
Navier-Stokes equations
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ISSN0022-0396
1090-2732
DOI10.1016/j.jde.2021.02.045

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Summary:We study the stationary Stokes and Navier-Stokes equations with nonhomogeneous Navier boundary conditions in a bounded domain Ω⊂R3 of class C1,1. We prove the existence and uniqueness of weak and strong solutions in W1,p(Ω) and W2,p(Ω) for all 1<p<∞, considering minimal regularity on the friction coefficient α. Moreover, we deduce uniform estimates for the solution with respect to α which enables us to analyze the behavior of the solution when α→∞.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.02.045