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In this 52-minute lecture, Alex Ionescu presents rigorous research on wave turbulence in water wave systems. Explore recent developments in this field that has gained significant attention, particularly in the context of semilinear models like Schrödinger equations and multi-dimensional KdV-type equations. Learn about the unique challenges posed by water wave equations, which are quasilinear in nature and cannot be solved through traditional Duhamel formula iterations due to derivative loss problems. Discover the innovative strategy developed by Ionescu and his collaborators Yu Deng and Fabio Pusateri that combines deterministic energy estimates with dispersive propagation of randomness arguments to overcome these challenges in the study of 2D gravity waves.
