Small H^{1/2} initial data and small multiplicative noise give global-in-time stochastic Navier-Stokes solutions with probability arbitrarily close to 1 on the three-dimensional torus.
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Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data
Small H^{1/2} initial data and small multiplicative noise give global-in-time stochastic Navier-Stokes solutions with probability arbitrarily close to 1 on the three-dimensional torus.