This article studies the interrelation between the determining modes property in the two-
dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the …

We consider the nonlinear Schr\" odinger equation on the $ d $-dimensional torus $\mathbb
T^ d $, with the nonlinearity of polynomial type $| u|^{2\sigma} u $. For any …

We establish a new criterion for exponential mixing of random dynamical systems. Our
criterion is applicable to a wide range of systems, including in particular dispersive …

In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic
nonlinear Schrodinger equation with either focusing or defocusing nonlinearity driven by …

Well-posedness à la Friedrichs is proved for a class of degenerate Kolmogorov equations
associated to stochastic Allen–Cahn equations with logarithmic potential. The …

We consider a stochastic nonlinear defocusing Schrödinger equation with zero-order linear
damping, where the stochastic forcing term is given by a combination of a linear …

The aim of this work is to investigate the influence of nonlinear multiplicative noise on the
Cauchy problem of the nonlinear fractional Schrödinger equation in the non-radial case …

This paper presents the support set and unique ergodicity of invariant measure given in
Ekren (2018) of stochastic KdV equation, which also offers an answer to the question about …

This paper is dedicated to radial solutions to the Cauchy problem for the fractional Hartree
equation with multiplicative noise. First, we establish a stochastic Strichartz estimate related …

The aim of this paper is to investigate the existence of optimal solutions for control problems
involving nonlinear stochastic Schrödinger equations perturbed by a multiplicative fractional …