Random attractors for damped stochastic fractional Schrödinger equation on ${\mathbb{R}}^n$

Abstract

We study the random attractors associated with the stochastic fractional Schrödinger equation on ${\mathbb{R}}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schrödinger equation with Gaussian noise, we show the existence and uniqueness of a global solution to the damped stochastic fractional nonlinear Schrödinger equation in $H^{\alpha }({\mathbb{R}}^n)$. Furthermore, we demonstrate that this equation defines an infinite-dimensional dynamical system, which possesses a global attractor in $H^{\alpha }({\mathbb{R}}^n)$.

arXiv admin note: text overlap with arXiv:2411.02781