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The Neumann problem for the planar Stokes system

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Abstract

The Neumann problem for the Stokes system is studied on bounded and unbounded domains with Ljapunov boundary (i.e. of class \({{\mathcal C}^{1,\alpha }}\)) in the plane. We construct a solution of this problem in the form of appropriate potentials and reduce the problem to an integral equation systems on the boundary of the domain. We determine a necessary and sufficient condition for the solvability of the problem. Then we study the direct integral equation method and prove that a solution of the corresponding integral equation can be obtained by the successive approximation.

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Authors and Affiliations

  1. Mathematical Institute Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    D. Medková

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  1. D. Medková
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Correspondence to D. Medková.

Additional information

This research was supported by GAČR Grant P201/11/1304 and RVO: 67985840.

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Medková, D. The Neumann problem for the planar Stokes system. Ann Univ Ferrara 58, 307–329 (2012). https://doi.org/10.1007/s11565-012-0154-8

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  • DOI: https://doi.org/10.1007/s11565-012-0154-8

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