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Two-dimensional gravity water waves with constant vorticity, I: Cubic lifespan
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https://doi.org/10.2140/apde.2019.12.903Abstract
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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