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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.
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.
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