科学研究
报告题目:

Stochastic Navier-Stokes equations via convex integration

报告人:

朱湘禅 研究员(中科院数学与系统科学研究院)

报告时间:

报告地点:

腾讯会议ID: 980 459 070

报告摘要:

In this talk I will talk about our recent work on the three dimensional stochastic Navier-Stokes equations via convex integration method.

First we establish non-uniqueness in law, existence and non-uniqueness of probabilistically strong solutions and non-uniqueness of the associated Markov processes. Second we prove existence of infinitely many stationary solutions as well as ergodic stationary solutions to the stochastic Navier-Stokes and Euler equations. Moreover, we are able to make conclusions regarding the vanishing viscosity limit and the anomalous dissipation.

Finally I will show global-in-time existence and non-uniqueness of probabilistically strong solutions to the three dimensional Navier--Stokes system driven by space-time white noise. In this setting, the convective term is ill-defined in the classical sense and probabilistic renormalization is required.

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