Mathematics Colloquium: Stochastic Navier-Stokes equations via convex integration
Xiangchan Zhu, Academy of mathematics and systems science, Chinese academy of sciences
Beijing, China.
Speaker |
Xiangchan Zhu, Academy of mathematics and systems science, Chinese academy of sciences
Beijing, China.
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When |
Nov 15, 2022
from 02:00 PM to 03:00 PM |
Where | via zoom |
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Abstract: 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.