Random uniform exponential attractors for non-autonomous stochastic discrete long wave-short wave resonance equations

Abstract

In this paper, we study the dynamical behavior of the non-autonomous stochastic discrete long wave-short wave resonance system with multiplicative white noise and quasi-periodic forces. Firstly, we prove the uniqueness and existence for the solution of the system, which generates a jointly continuous random dynamical system $ \Phi $. Secondly, we prove the existence of a uniform absorbing random set for $ \Phi $ and estimate tail of the solution. Thirdly, we prove the Lipschitz continuity of the skew-product cocycle $ \pi $ defined on an extended space. Fourthly, we prove that the expectation of some random variables are bounded. Finally, we prove the existence of a random uniform exponential attractor for the considered system.