Random uniform exponential attractors for non-autonomous stochastic Schrödinger lattice systems in weighted space

Abstract

We mainly study the existence of random uniform exponential attractors for non-autonomous stochastic Schrödinger lattice system with multiplicative white noise and quasi-periodic forces in weighted spaces. Firstly, the stochastic Schrödinger system is transformed into a random system without white noise by the Ornstein-Uhlenbeck process, whose solution generates a jointly continuous non-autonomous random dynamical system Φ. Secondly, we prove the existence of a uniform absorbing random set for Φ in weighted spaces. Finally, we obtain the existence of a random uniform exponential attractor for the considered system Φ in weighted space.

Keywords

• non-autonomous schrödinger lattice system
• random uniform exponential attractor
• weighted space
• quasi-periodic force
• multiplicative white noise