We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional
cubic wave equation, which is also known as the hyperbolic Φ 3 4-model. This result is the …

We consider the defocusing nonlinear Schr\" odinger equation on $\mathbb {T}^ 2$ with
Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect …

A fundamental question in wave turbulence theory is to understand how the wave kinetic
equation describes the long-time dynamics of its associated nonlinear dispersive equation …

We consider the cubic nonlinear Schrödinger equation posed on the spatial domain R× Td.
We prove modified scattering and construct modified wave operators for small initial and …

We consider the Cauchy problem of the cubic nonlinear Schrödinger equation (NLS) $:
i\partial _t u+\Delta u=\pm| u|^{2} u $ on $\mathbb {R}^ d $, $ d\geq 3$, with random initial …

Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity
II: Dynamics Page 1 © 2023 European Mathematical Society Published by EMS Press and …

In this paper, we consider the defocusing Hartree nonlinear Schrödinger equations on T 3
with real-valued and even potential V and Fourier multiplier decaying such as| k|− β. By …

We introduce a randomization of a function on ℝ d R^ d that is naturally associated to the
Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized …

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
| Probability Theory and Related Fields Skip to main content SpringerLink Log in Menu Find a …

We consider the Cauchy problem for the defocusing cubic nonlinear Schrödinger equation
in four space dimensions and establish almost sure local well-posedness and conditional …