PDE/Analysis Seminar
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Speaker: Jiajun Wang (New York University) Title: Bilinear Shell-Type Decoupling and Applications to Dispersive Equations Abstract: The periodic Zakharov system couples Schrödinger and wave equations, leading to a special shell-type structure in frequency space. Motivated by this observation, I study bilinear decoupling estimates for the paraboloid when the Fourier supports are restricted to thin spherical shells of two different radii. I establish sharp bilinear shell-type decoupling estimates that improve upon applying linear shell decoupling separately to the two factors. As applications, I obtain bilinear Strichartz estimates on tori, with further improvements on the square torus using a refined circle method. These estimates are motivated by the study of nonlinear smoothing for the periodic Zakharov system.
