On two-dimensional gravity water waves with angled crests
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
Local well-posedness results
Water wave modelling
Low-regularity Sobolev space
76N10 - Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
76B15 - Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]
In this talk, I will present our recent work on the local in time existence of two-dimensional gravity water waves with angled crests. Specifically, we construct an energy functional $E(t)$ that allows for angled crests in the interface. We show that for any initial data satisfying $E(0)<\infty$, there is $T>0$, depending only on $E(0)$, such that the water wave system is solvable for time $t\in [0, T]$. Furthermore we show that for any smooth initial data, the unique solution of the 2d water wave system remains smooth so long as $E(t)$ remains finite.
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