Markov selection and W-strong Feller for 3D stochastic primitive equations  

作　　者：DONG Zhao ZHANG RangRang 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2017年第10期1873-1900,共28页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11431014,11371041,11401557 and 11271356);the Fundamental Research Funds for the Central Universities(Grant No.0010000048);Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182);the Applied Mathematical Research for the Important Strategic Demand of China in Information Science and Related Fields(Grant No.2011CB808000)

摘　　要：This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.

关 键 词：primitive equations Markov selection W-strong Feller 

分 类 号：O211.6[理学—概率论与数理统计]