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Two-dimensional
gravity water waves with constant vorticity, I: Cubic
lifespan
Mihaela Ifrim and Daniel Tataru |
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Vol. 12 (2019), No. 4, 903–967
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DOI: 10.2140/apde.2019.12.903
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Abstract |
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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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Keywords
gravity waves, constant vorticity, normal forms, modified
energy
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Mathematical Subject Classification 2010
Primary: 35Q35
Secondary: 42B37, 76B15
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Milestones
Received: 17 February 2017
Revised: 22 May 2018
Accepted: 14 July 2018
Published: 20 October 2018
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Authors |
| Mihaela Ifrim | |
| Department of Mathematics University of California at Berkeley Berkeley, CA United States |
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| Daniel Tataru | |
| Department of Mathematics University of California at Berkeley Berkeley, CA United States |
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