李扬荣

(报告时间 10:00-10:30)

西南大学

报告题目：Longtime robustness of pullback random attractors

摘要: In this talk, we focus on the semi-continuity of a pullback random attractor (PRA) at infinite time. We first establish the criteria for backward compactness of a PRA from a backward limit-set compact cocycle. We then prove that backward compactness of a PRA is a necessary and sufficient condition such that its time-fibers are upper semi-continuous at negative infinity, and obtain the minimal compact limit-set. We further obtain the maximal limit-set in the lower semi-continuity sense. The abstract results are illustrated in the contexts of stochastic magneto-hydrodynamics equations. Some further questions (or subjects) are proposed.

周国立

(报告时间 10:40-11:10)

重庆大学

报告题目：ON THE BACKWARD UNIQUENESS OF THE STOCHASTIC PRIMITIVE EQUATIONS WITH ADDITIVE NOISE

摘  要:The previous works focus on the uniqueness for the initial-value problems of stochastic primitive equations. Uniqueness for the initial-value problems means that if the two initial conditions are the same, then the two solutions coincide with each other. However there is no work to answer what will happen to the solutions if the two initial conditions are different. This problem for the stochastic three dimensional primitive equations is addressed by the backward uniqueness established in this article. The backward uniqueness means that if two solutions intersect at time t > 0; then they are equal everywhere on the interval (0; t): In other words, given two different initial-value conditions, the corresponding two solutions will never cross in the future. Hence this article can be viewed as a further study of the dependence  of the solutions on the initial data.

谷安辉

(报告时间 11:20-11:50)

西南大学

报告题目Random Attractors for SPDEs with General Diffusion Terms

摘要：Three approaches introduced first to obtain the existence of random attractors for SPDEs with general diffusion terms. As an application, the existence and approximation of random attractors for the non-autonomous 2D Navier-Stoke equation driven by colored noise were presented.