Wednesday, May 12, 2021 - 14:00 in ZOOM - Video Conference
Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness
A talk in the Bielefeld Stochastic Afternoon series by
Rongchan Zhu from Beijing Institute of Technology
| Abstract: |
We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result in particular implies non-uniqueness in law. Second, we prove non-uniqueness of the associated Markov processes in a suitably chosen class of analytically weak solutions satisfying a relaxed form of an energy inequality. Translated to the deterministic setting, we obtain non-uniqueness of the associated semiflows.
This talk is based on joint work with Martina Hofmanova and Xiangchan Zhu.
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password. (New meeting details since April 1!)
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