APNANAMar 18, 2013

Variational views of stokeslets and stresslets

arXiv:1303.429920 citationsh-index: 26
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Provides a novel variational framework for Stokes layer potentials, but the results are not new, making it an incremental contribution for mathematicians working on boundary integral methods.

The paper develops a self-contained variational theory for Stokes layer potentials on Lipschitz boundaries, proving Calderón projector properties and linking to integral forms via Lamé and Laplace operators. The approach is novel but all results are known for smooth domains and mostly known for non-smooth domains.

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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