Random attractors and their higher-order regularity properties are studied for stochastic reaction–diffusion equations on time-varying domains. Some new a priori estimates for the difference of solutions near the initial time and the continuous dependence in initial data in [Formula: see text] are proved. Then attraction of the random attractors in the higher integrability space [Formula: see text] for any [Formula: see text] and the regular space [Formula: see text] is established.

中文翻译：

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时变域上随机反应扩散方程的高阶正则吸引子

针对时变域上的随机反应扩散方程研究了随机吸引子及其高阶规律性。证明了[公式：见正文]中对初始时间附近解的差异和初始数据的连续依赖性的一些新的先验估计。然后对任意[公式：见文]和正则空间[公式：见文]建立高可积空间[公式：见文]中的随机吸引子的吸引力。