The stochastic coupled Kuramoto–Sivashinsky and Ginzburg–Landau equations (KS-GL) perturbed by additive noises is investigated in this paper. By making careful analysis, we first consider the existence and uniqueness of the solution with initial-boundary condition, and then we establish a random attractor for the stochastic KS–GL equations in $X=L^{2} \times H^{-1}$.

中文翻译：

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随机耦合的Kuramoto–Sivashinsky和Ginzburg–Landau方程的渐近行为

本文研究了加性噪声扰动的随机耦合的Kuramoto–Sivashinsky和Ginzburg–Landau方程（KS-GL）。通过仔细分析，我们首先考虑具有初始边界条件的解的存在性和唯一性，然后在$ X = L ^ {2} \ times H ^ {-中建立随机的KS-GL方程的随机吸引子。 1} $。