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An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions. (English) Zbl 0734.35077

The paper gives a representation of the solution of the resolvent problem for the Stokes-system \[ (\lambda I-\Delta)u+\nabla \pi =f,\quad div u=0,\quad u|_{\partial \Omega}=0 \] on bounded or exterior domains \(\Omega \subset {\mathbb{R}}^ 3\) by potential theoretic methods.
This can be found also in P. Deuring [Math. Methods Appl. Sci. 13, 323-333, and 335-349 (1990; Zbl 0726.35098 and Zbl 0726.35099)] together with explicit estimates in \(L_ p\)-spaces.
The paper ends with boundary integral equations for the case \(f=0\) and Dirichlet- or Neumann type boundary conditions.

MSC:

35Q30 Navier-Stokes equations
35J25 Boundary value problems for second-order elliptic equations
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References:

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