Speaker: Zhu Rongshan, Professor, Beijing Institute of Technology

Date: Sept. 22, 2021

Time: 19:00

Location: Tencent Meeting, ID: 488 2330 4823

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 semi flows.

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