Uniform attractors for non-autonomous Zakharov lattice systems with multiplicative white noise

In this paper, we first give the existence criteria of the random uniform attractors and random uniform exponential attractors for jointly continuous random dynamical systems on the product space of weighted spaces of infinite sequences. Then we consider the existence of the random uniform attractors for Zakharov lattice systems with almost periodic external forces and multiplicative white noise. Finally, we consider the existence of the random uniform exponential attractors for Zakharov lattice systems with quasi-periodic external forces and multiplicative white noise. The used method is to transform the Zakharov lattice stochastic differential equations (SDE) with white noise into the Zakharov lattice random differential equations (RDE) with random coefficients but without white noise by constructing a reversible variable substitution through a stationary Ornstein-Uhlenbeck process. It is proved that the solutions of the RDE type lattice systems and the SDE type lattice systems can generate two conjugate jointly continuous random dynamical systems. The existence of the uniformly closed absorbing random set of the system is proved, the tail of the 解 is estimated, and the Lipschitz continuity and the random squeezing 性质 of the system are verified.