We study global-in-time dynamics of the stochastic nonlinear wave equations (SNLW) with
an additive space-time white noise forcing, posed on the two-dimensional torus. Our goal in …

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 …

We consider the defocusing nonlinear wave equation of power-type on ℝ3. We establish an
almost sure global existence result with respect to a suitable randomization of the initial …

Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized
version of the three-dimensional stochastic nonlinear wave equation with quadratic …

We study the nonlinear wave equation (NLW) on the two-dimensional torus T 2 with
Gaussian random initial data on H s (T 2)× H s− 1 (T 2), s< 0, distributed according to the …

We prove almost sure global well-posedness of the energy-critical defocusing quintic
nonlinear wave equation on R 3 with random initial data in H s (R 3)× H s− 1 (R 3) for s> 1 2 …

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 …

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 …

A Remark on Norm Inflation with General Initial Data for the Cubic Nonlinear Schrödinger
Equations in Negative Sobolev Spaces Page 1 Funkcialaj Ekvacioj, 60 (2017) 259–277 A …

We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the
dynamics of the three-dimensional defocusing cubic nonlinear wave equation. As in …