Work

Well-Posedness of a Generalized Stokes Operator on Smooth Bounded Domains via Layer-Potentials

Year: 2026

Type: article

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.

Source: Journal of Mathematical Fluid Mechanics

DOI: 10.1007/s00021-026-01021-w

Authors: Mirela Kohr, Victor Nistor, Wolfgang L. Wendland

Institutions: Babeș-Bolyai University, Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Université de Lorraine, University of Stuttgart

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funder: Agence Nationale de la Recherche