Variational views of stokeslets and stresslets

2013/03/18 by Francisco‐Javier Sayas, Sayas, Francisco-Javier, Virginia Selgás +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1303.4299

openalex publication_date 2013/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a self-contained variational theory of the layer potentials for the Stokes problem on Lipschitz boundaries. We use these weak definitions to show how to prove the main theorems about the associated Calderón projector. Finally, we relate these variational definitions to the integral forms. Instead of working these relations from scratch, we show some formulas parametrizing the Stokes layer potentials in terms of those for the Lamé and Laplace operators. While all the results in this paper are well known for smooth domains, and most might be known for non-smooth domains, the approach is novel a gives a solid structure to the theory of Stokes layer potentials.

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• Well-posedness of a generalized Stokes operator on smooth bounded domains via layer-potentials

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