Well-Posedness of a Generalized Stokes Operator on Smooth Bounded Domains via Layer-Potentials
Abstract
Abstract We prove the invertibility of the relevant single and double layer potentials associated to some generalizations of the Stokes operator on bounded domains. In order to do that, we first develop an “algebra tool kit” to deal with limit and jump relations of layer operators. We do that first on $$\mathbb {R}^{n}$$ R n for operators acting on a distribution supported on $$\{x_{n} = 0\}$$ { x n = 0 } and then in general on (possibly non-compact) manifolds. We use these results to study the limit and jump relations of the layer potential operators associated to our generalized Stokes operators. As an application, we obtain well-posedness results for the Stokes system.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Numerical methods in inverse problems
Navier-Stokes equation solutions
Publication details
- Journal / source
- Journal of Mathematical Fluid Mechanics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 28
- Issue
- 2
- Publication date
- 21 April 2026
- Language
- EN