Weighted Hilbert spaces for the Stationary exterior Stokes problem with Navier slip boundary conditions

Abstract : In this paper, we analyse the exterior Stokes problem with the Navier slip boundary conditions, describing the flow of a viscous and incompressible fluid pas an obstacle where it is assumed that the fluid may slip at the boundary. Because the flow domain is unbounded, we set the problem in weighted spaces in order to control the behavior at infinity of the solutions. This functional framework also allows to prescribe various behaviors at infinity of the solutions (growth or decay). Existence and uniqueness of solutions are shown in a Hilbert setting which gives the tools for a possible numerical analysis of the problem. Weighted Korn's inequalities are the key point in order to study the variational problem.
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Contributor : Ulrich Razafison <>
Submitted on : Saturday, March 23, 2019 - 11:56:02 AM
Last modification on : Thursday, March 28, 2019 - 2:42:06 AM

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Anis Dhifaoui, Mohamed Meslameni, Ulrich Razafison. Weighted Hilbert spaces for the Stationary exterior Stokes problem with Navier slip boundary conditions. Journal of Mathematical Analysis and Applications, Elsevier, 2019, 472 (2), pp.1846-1871. ⟨10.1016/j.jmaa.2018.12.026⟩. ⟨hal-01788047v3⟩

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