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

Zhao Dong, Rang Rang Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1873-1900
Number of pages28
JournalScience China Mathematics
Volume60
Issue number10
DOIs
Publication statusPublished - 1 Oct 2017
Externally publishedYes

Keywords

  • Markov selection
  • W-strong Feller
  • primitive equations

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