Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations-China University of Mining & Technology-Beijing-China University of Mining & Technology-Beijing

Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations

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speaker: Yachun Li

time: 2024.12.02,10:00-11:30AM

place: Yifu Building 1537

Abstract：

This talk concerns the 3D forced stochastic Navier-Stokes equation driven by additive noise. By constructing an appropriate forcing term, we prove that there exist distinct Leray solutions in the probabilistically weak sense. In particular, the joint uniqueness in law fails in the Leray class. The non-uniqueness also displays in the probabilistically strong sense in the local time regime, up to stopping times. Furthermore, we discuss the optimality from two different perspectives: sharpness of the hyper-viscous exponent and size of the external force. This is a joint work with Elia Brué, Rui Jin, and Deng Zhang.

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