Large deviations principle via Malliavin calculus for the Navier--Stokes system driven by a degenerate white-in-time noise

：彭旭辉（湖南师范大学）
：2022-05-20 16:00
：腾讯会议ID：518884178（无密码）

报告人：彭旭辉（湖南师范大学）

时  间：5月20日下午16:00

地  点：腾讯会议ID：518884178（无密码）

内容摘要:

The purpose of this paper is to establish the Donsker--Varadhan type large deviations principle (LDP) for the two-dimensional stochastic Navier--Stokes system. The main novelty is that the noise is assumed to be highly degenerate in the Fourier space. The proof is carried out by using a criterion for the LDP developed in [Jak\v si\'c et.al.\emph{Nonlinearity},31(2):540-596,2018] in a discrete-time setting and extended in [Martirosyan and Nersesyan. \emph{Ann.Inst.Henri Poincar\'{e} Probab. Stat.}, 54(4):2002-2041,2018] to the continuous-time. One of the main conditions of that criterion is the uniform Feller property for the Feynman-Kac semigroup,which we verify by using Malliavin calculus. This work is based on joint work with Vahagn Nersesyan and Lihu Xu.

个人简介：

彭旭辉，湖南师范大学副教授，湖南省普通高校青年骨干教师。2014年博士毕业与中科院数学与系统科学研究院。主要研究方向为随机分析，在《Journal of the European Mathematical Society》《Annales de l’Institut Henri Poincar´e Probabilit´es et Statistique》《Journal of Differential Equations》等期刊上发表或者接受发表论文近20篇。现主持国家自然科学基金面上项目一项。

 

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