| 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 Bru$\`e$, Rui Jin, and Deng Zhang. |
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