Analysis Seminar

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On the derivation of the inhomogeneous kinetic wave equation

Speaker: Ioakeim AMPATZOGLOU, Courant Institute

Location: Warren Weaver Hall 312

Date: Thursday, November 11, 2021, 11 a.m.

Synopsis:

The topic of this talk will be the validity  of a kinetic description for wave turbulence of a model quadratic dispersive equation. We focus on deriving an inhomogeneous (transport) effective equation for the Wigner transform of the microscopic model solution, up to a small polynomial loss of the kinetic time. We will present nonlinearities where the kinetic description holds and  cases where it might fail. We achieve that by examining the convergence of the Dyson series under random data in the weakly nonlinear regime.