Vol. 12, No. 4, 2019

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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

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.

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gravity waves, constant vorticity, normal forms, modified energy
Mathematical Subject Classification 2010
Primary: 35Q35
Secondary: 42B37, 76B15
Received: 17 February 2017
Revised: 22 May 2018
Accepted: 14 July 2018
Published: 20 October 2018
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