Invariant Gibbs Measures And Almost Surely Global Well-posedness For The Periodic Ostrovsky Equation

We consider the Cauchy problem of the Ostrovsky model for nonlinear waves with periodic boundary condition,and random initial data of low regularity.We first prove that this Cauchy problem is locally well-posed in Hs(T)with s ≥-1/2,and globally well-posed almost surely with a large set of random data in ∩-1/2≤s<1/2 Hs(T).Then,we show that the Gibbs measure is invariant under the flow,for random data in ∩1/6<s<1/2 Hs(T).The key ingredients are a Strichartz type estimate established in this paper and certain large deviation estimates.In Chapter one,firstly,we introduce the development background and significance of the Ostrovsky equation and then give the main problems and conclusions.In Chapter two,firstly,we give some notations and lemmas which are used in this paper and establish two important bilinear estimates,secondly,we prove that the Cauchy problem for the periodic deterministic Ostrovsky equation is locally well-posed in Hs(T)with s ≥-1/2,two theorems are proved in the last,which are based on above knowledge.