Courant PIs Workshop 2022
Abstract: We introduce the Wick NLS and study its wave kinetic theory in both the homogeneous setting and the inhomogeneous setting. The Wick NLS can be regarded as a renormalization of the NLS by eliminating all self-interactions from the equation. Consequently it enjoys a much better algebraic structure and has significantly easier estimates. Using ideas from microlocal analysis, we derive three wave kinetic equations—(WK0), (WK1) and (WK2)—for the Wick NLS.
Precisely, the equation (WK0) describes the effective dynamics in the homogeneous setting, and (WK1) in the inhomogeneous setting. The equation (WK2) gives a finer characterization of the effective dynamics by applying second microlocalization to the Wick NLS. This is a joint work with Zaher Hani and Jalal Shatah.
You can view slides from the presentation here.