带可乘白噪音的非线性耦合复Ginzburg-Landau方程组的随机吸引子

Random attractor for nonlinear coupled complex Ginzburg-Landau equations with multiplicative white noise

研究一类带可乘白噪音的非线性耦合复Ginzburg-Landau方程组的随机吸引子,采用解的先验估计和Ball创建的能量方程方法,证明了在初始条件和周期边界条件下它的随机吸引子的存在性。证明过程分成3个步骤:首先对方程组的可乘白噪音进行预处理,使得随机微分项消失;其次证明方程组对应的随机动力系统在H中和V中存在吸收集,最后得到Ginzburg-Landau方程组在H中存在随机吸引子。

In this paper,the random attractor of the nonlinear coupled complex Ginzburg-Landau equations with multiplicative white noise are investigated.Under the initial condition and periodic boundary condition,the existence of random attractors for the complex equations is proven using the prior estimate of solutions and the method of energy equations introduced by Ball.It could be divided into three steps:first,it preprocesses the multiplicative white noise terms,which makes the stochastic differential item disappear.And then,the existence of absorbing set of stochastic dynamical system associated with the nonlinear coupled complex Ginzburg-Landau equations in H and V is proven.Finally,it proves the existence of random attractor when equations are in H.