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SeMA Journal

, Volume 63, Issue 1, pp 65–90 | Cite as

Variational views of stokeslets and stresslets

  • Francisco-Javier SayasEmail author
  • Virginia Selgas
Article

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 and gives a solid structure to the theory of Stokes layer potentials.

Keywords

Stokes flow Potential theory Boundary integral equations 

Mathematics Subject Classification

31B10 76D07 

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Copyright information

© Sociedad Española de Matemática Aplicada 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Departamento de MatemáticasUniversidad de OviedoOviedoSpain

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