Establishes local wellposedness for 2D water waves with cornered/cusped interfaces that is uniform in gravity g (including g=0), with blowup examples proving optimality of the result.
Blow-up conditions for gravity water-waves
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abstract
We exhibit blow-up conditions for the gravity water-waves equations in any dimension and in domains with arbitrary bottoms. We follow the method by Alazard, Burq and Zuily of using a paradifferential reduction of the equations and derive precise a priori Sobolev estimates. Those estimates are then used to prove three different blow-up conditions where neither the boundedness of the curvature of the surface nor the boundedness in time of the Lipschitz norm of the velocity are needed.
fields
math.AP 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
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Uniform in gravity estimates for 2D water waves
Establishes local wellposedness for 2D water waves with cornered/cusped interfaces that is uniform in gravity g (including g=0), with blowup examples proving optimality of the result.