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.
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Partially supported by the NSF (DMS 1216356). Partially supported by MICINN (Project MTM2010-21135-C021-01) and the Universidad de Oviedo ‘Ayudas de Movilidad de Excelencia’ Program.
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Sayas, FJ., Selgas, V. Variational views of stokeslets and stresslets. SeMA 63, 65–90 (2014). https://doi.org/10.1007/s40324-014-0013-x
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DOI: https://doi.org/10.1007/s40324-014-0013-x