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Communications in Mathematical Physics

, Volume 330, Issue 2, pp 859–886 | Cite as

Capillary–Gravity Water Waves with Discontinuous Vorticity: Existence and Regularity Results

  • Anca-Voichita MatiocEmail author
  • Bogdan-Vasile Matioc
Article

Abstract

In this paper we construct periodic capillarity–gravity water waves with an arbitrary bounded vorticity distribution. This is achieved by re-expressing, in the height function formulation of the water wave problem, the boundary condition obtained from Bernoulli’s principle as a nonlocal differential equation. This enables us to establish the existence of weak solutions of the problem by using elliptic estimates and bifurcation theory. Secondly, we investigate the a priori regularity of these weak solutions and prove that they are in fact strong solutions of the problem, describing waves with a real-analytic free surface. Moreover, assuming merely integrability of the vorticity function, we show that any weak solution corresponds to flows having real-analytic streamlines.

Keywords

Vorticity Weak Solution Water Wave Local Bifurcation Water Wave Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für MathematikUniversität WienViennaAustria

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