Random attractor and upper semi-continuity for Zakharov lattice system with multiplicative white noise

Abstract

In this paper, we study the long-term asymptotic behaviour of solutions to the stochastic Zakharov lattice equation with multiplicative white noise. We first transfer the stochastic lattice equation into a random lattice equation and prove the existence and uniqueness of solutions which generate a random dynamical system. Then we consider the existence of a tempered random bounded absorbing set and a random attractor for the system. Finally we establish the upper semi-continuity of random attractor to the global attractor of the limiting system as the coefficients of the white noise terms tend to zero.