For every divergence-free, mean-free initial condition in L2, the 3D stochastic Navier-Stokes equations with Lipschitz multiplicative noise admit infinitely many global probabilistically strong weak solutions, implying non-uniqueness in law.
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Nonuniqueness in law of stochastic 3d navierstokes equations with general multiplicative noise
For every divergence-free, mean-free initial condition in L2, the 3D stochastic Navier-Stokes equations with Lipschitz multiplicative noise admit infinitely many global probabilistically strong weak solutions, implying non-uniqueness in law.