Vol. 12, No. 4, 2019

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ISSN: 1948-206X (e-only)
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Two-dimensional gravity water waves with constant vorticity, I: Cubic lifespan

Mihaela Ifrim and Daniel Tataru

Vol. 12 (2019), No. 4, 903–967
DOI: 10.2140/apde.2019.12.903
Abstract

This article is concerned with the incompressible, infinite-depth water wave equation in two space dimensions, with gravity and constant vorticity but with no surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove local well-posedness for large data, as well as cubic lifespan bounds for small-data solutions.

Keywords
gravity waves, constant vorticity, normal forms, modified energy
Mathematical Subject Classification 2010
Primary: 35Q35
Secondary: 42B37, 76B15
Milestones
Received: 17 February 2017
Revised: 22 May 2018
Accepted: 14 July 2018
Published: 20 October 2018
Authors
Mihaela Ifrim
Department of Mathematics
University of California at Berkeley
Berkeley, CA
United States
Daniel Tataru
Department of Mathematics
University of California at Berkeley
Berkeley, CA
United States