Vorticity jumps in steady water waves

Walter A. Strauss

doi:10.3934/dcdsb.2012.17.1101

Article Contents

2012, Volume 17, Issue 4: 1101-1112. Doi: 10.3934/dcdsb.2012.17.1101

This issue Previous Article Preface Next Article Well-posedness of a model for water waves with viscosity

Vorticity jumps in steady water waves

Walter A. Strauss^1,

1.
Brown University, Department of Mathematics and Lefschetz Center for Dynamical Systems, Providence, RI 02912

Received: December 2010

Revised: September 2011

Published: June 2012

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Abstract

There exists a large family of water waves with jump discontinuities in the vorticity. These waves travel at a constant speed. They are two-dimensional, periodic, symmetric, and subject to the influence of gravity. Some of them have large amplitudes. Their existence is proven using local and global bifurcation theory, together with elliptic theory of weak solutions with nonlinear boundary conditions.

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Mathematics Subject Classification: Primary: 76B15, 35J66; Secondary: 35Q35.

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