Very weak solution for the exterior stationary Stokes equations with Navier 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.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Advanced Numerical Methods in Computational Mathematics
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 31
- Issue
- 0
- Pages
- 1–17
- Publication date
- 11 February 2026
- Language
- EN