Random exponential attractor for a non-autonomous Zakharov lattice system with multiplicative white noise

Abstract

We prove the existence of a random exponential attractor for a non-autonomous Zakharov lattice system with multiplicative white noise. We first transfer the stochastic lattice system into an equivalent random lattice system whose solutions generate a continuous cocycle on a phase space of infinite sequences. Then we estimate the tail of solutions for the random system. We next verify that the continuous cocycle satisfies the Lipschitz continuity and the random squeezing property on a tempered random closed absorbing set. Finally, we check the boundedness of the expectation of some random variables and obtain the existence of a random exponential attractor.