Very weak solution for the exterior stationary Stokes equations with Navier slip boundary condition

Abstract

In some problems of fluid mechanics, it is possible to be confronted with data that are not regular, that is why we are interested here in the search for the so-called very weak solutions for the stationary Stokes problem with Navier-type boundary conditions in a three-dimensional exterior domain. The problem describes the flow of a viscous and incompressible fluid past an obstacle where we assume that the fluid may slip on the boundary of the obstacle. Because the flow domain is unbounded, we set the problem in weighted Sobolev spaces in order to control the behavior at infinity of the solutions. Our purpose is to prove the existence and the uniqueness of a very weak solution in a Hilbertian framework.

Very weak solution for the stationary exterior Stokes equations with non‐standard boundary conditions in Lp‐theory

“…The following lemmas state some properties related to the space T p 2 (Ω); these are extensions of the properties given in Dhifaoui. 40 First, we will characterize the dual space of…”

“…34,35 Amrouche and Seloula 36 proved the existence and uniqueness of weak, strong, and very weak solutions for the Stokes equations with Navier-type boundary condition. In the case when Ω is an unbounded domain, we can mention Amrouche et al [37][38][39] and Dhifaoui 40 and references therein.…”

Irreversibility Analysis of Electromagnetic Hybrid Nanofluid Over a Stretchable Surface with Cattaneo-Christov Heat Flux Model: Finite Element Approach

“…Arif et al [55] analyzed SBC of Non-Newtonian rheology of lubricant. Dhifaoui [56] illustrated a weak solution for the outside static Stokes equations with SBC. Zeb et al [57] proposed the SBC on Non-Newtonian Ferrofluid over an extending slip.…”