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Periodic Traveling Gravity Water Waves with Discontinuous Vorticity

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Abstract

We use elliptic theory to prove the existence of steady two-dimensional periodic waterwaves of large amplitude in a flowwith an arbitrary bounded but discontinuous vorticity. This is achieved by developing a local and global bifurcation construction of weak solutions of the elliptic partial differential equations that are relevant to this hydrodynamical context.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090, Vienna, Austria

    Adrian Constantin

  2. Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Box 1917, Providence, RI, 02912, USA

    Walter Strauss

Authors
  1. Adrian Constantin
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  2. Walter Strauss
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Corresponding author

Correspondence to Walter Strauss.

Additional information

Communicated by P. Rabinowitz

The research of the first author was supported by the WWTF and that of the second author by NSF Grant DMS-1007960.

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Constantin, A., Strauss, W. Periodic Traveling Gravity Water Waves with Discontinuous Vorticity. Arch Rational Mech Anal 202, 133–175 (2011). https://doi.org/10.1007/s00205-011-0412-4

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  • DOI: https://doi.org/10.1007/s00205-011-0412-4

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