PDE/Analysis Seminar

About this event

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.