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math.AP2026
Local-in-Time Existence of solutions to the Gravity Water Wave Kinetic Equation
Yulin Pan, Xiaoxu Wu
In this paper, we study the Cauchy problem for the four-wave kinetic equation describing the weak turbulence of gravity water waves. The mathematical challenges of this analysis st…
math.AP2024
Decomposition of global solutions for a class of nonlinear wave equations
Georgios Mavrogiannis, Avy Soffer, Xiaoxu Wu
In the present paper we consider global solutions of a class of non-linear wave equations of the form \begin{equation*} \Box u= N(x,t,u)u, \end{equation*} where the nonlinearity~$…
math.AP2022
Boundedness of the Scattering Wave Operators of Schrödinger Dynamics -- Part 2
Avy Soffer, Xiaoxu Wu
We give another proof of the boundedness of scattering wave operators, at the low frequency part of the data. The proof also allows the control of the commutator of multiplic…