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Explore a lecture on the quartic integrability and long-term existence of steep water waves in two dimensions. Delve into the work of Dyachenko & Zakharov from 1994, which established the absence of 3-wave interactions and the vanishing of 4-wave interaction coefficients on the non-trivial resonant manifold for weakly nonlinear 2D infinite depth water waves. Examine a recent result that proves this partial integrability from a different perspective, involving the construction of a sequence of energy functionals in physical space using the Riemann mapping variable. Learn about the long-time existence results for 2D water wave equations, which allow for arbitrary large steepnesses of the interface and initial velocities. Gain insights from Sijue Wu of the University of Michigan during this hour-long presentation at the Institut des Hautes Etudes Scientifiques (IHES).
