Stokes and Navier-Stokes equations with Navier boundary conditions

P Acevedo Tapia,C Amrouche,C Conca,A Ghosh

doi:10.1016/j.jde.2021.02.045

Stokes and Navier-Stokes equations with Navier boundary conditions

P Acevedo Tapia, C Amrouche + Show 2 more

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https://doi.org/10.1016/j.jde.2021.02.045

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Journal: Journal of Differential Equations	Publication Date: Mar 16, 2021
Citations: 23	License type: publisher-specific-oa

Affiliation: National Polytechnic School, Center for Mathematical Modeling, Laboratory of Mathematics and their Applications, French National Centre for Scientific Research, University of the Basque Country

#Navier Boundary Conditions #Navier-Stokes Equations + Show 8 more

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Abstract

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→∞.

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