Invariant Gibbs Measures and Almost Surely Global well-posedness for the Periodic Ostrovsky Equation

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摘要：

考虑周期Ostrovsky方程的随机初值的柯西问题u_t-β_x^3u-γ_x-1u+1/2_x(u^2)=0.首先证明在Hs(T)中当s≥-1/2的柯西问题是局部适定的和在∩-1/2≤s<12H^s(T)中随机初值的柯西问题是几乎整体适定的.对于在∩1/6

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 5 , and globally well-posed almost surely with a large set of random data in .Then, we show that the Gibbs measure is invariant under the flow , for random data in . The key ingredients are a Strichartz type estimate established in this paper and certain large deviation estimates.

作者：

闫威王宗敏

Yan Wei Wang Zongmin(College of Mathematics and Information Science, Henan Normal University ？Xinxiang 453007 , Chin)

机构地区：

betway官方app 数学与信息科学学院

出处：

《betway官方app 学报：自然科学版》 CAS 北大核心 2017年第4期15-28,共14页

基金国家自然科学基金(11401180)

关键词：

OSTROVSKY方程几乎整体适定性 Gibbs测度

Ostrovsky equation for nonlinear waves almost surely global well-posedness Gibbs measures

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