Our goal in this paper is to initiate the rigorous investigation of wave turbulence and
derivation of wave kinetic equations (WKEs) for water waves models. This problem has …

We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian
perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall …

We consider quasilinear, Hamiltonian perturbations of the cubic Schrödinger and of the
cubic (derivative) Klein–Gordon equations on the d-dimensional torus. If 𝜖≪ 1 is the size of …

We consider the gravity water waves system with a periodic one-dimensional interface in
infinite depth and we establish the existence and the linear stability of small amplitude, quasi …

We consider the gravity water waves system with a periodic one‐dimensional interface in
infinite depth and give a rigorous proof of a conjecture of Dyachenko‐Zakharov [16] …

We provide an accurate description of the long time dynamics of the solutions of the
generalized Korteweg–De Vries and Benjamin–Ono equations on the one dimension torus …

We consider the semi-linear beam equation on the d dimensional irrational torus with
smooth nonlinearity of order n-1 n-1 with n ≥ 3 n≥ 3 and d ≥ 2 d≥ 2. If ε ≪ 1 ε≪ 1 is the …

We consider the gravity water waves system with a periodic one-dimensional interface in
infinite depth and we establish the existence and the linear stability of small amplitude, quasi …

We study a fundamental model in fluid mechanics—the 3D gravity water wave equation, in
which an incompressible fluid occupying half the 3D space flows under its own gravity. In …

This article represents the first installment of a series of papers concerned with low regularity
solutions for the water wave equations in two space dimensions. Our focus here is on sharp …