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

2021/11/10 by Anis Dhifaoui, Dhifaoui, Anis
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.05824

openalex publication_date 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Singular weak solutions near boundaries in a half space away from localized force for the Stokes and Navier-Stokes equations
• Stokes and Navier-Stokes equations with Navier boundary condition
• Exterior Navier-Stokes flows for bounded data
• Existence, regularity and uniqueness of weak solutions for a class of incompressible generalized Navier-Stokes system with slip boundary conditions in ℝ³₊
• A Study of the Navier-Stokes Equations with the Kinematic and Navier Boundary Conditions