For subcritical fractional dissipation s in (1,2) and any H^sigma initial data with sigma>3, and for critical s=1 with small data and noise, the 3D primitive equations with Stratonovich transport noise have unique local pathwise solutions.
On the well-posedness of stochastic Boussinesq equations wit h transport noise
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On the local well-posedness of fractionally dissipated primitive equations with transport noise
For subcritical fractional dissipation s in (1,2) and any H^sigma initial data with sigma>3, and for critical s=1 with small data and noise, the 3D primitive equations with Stratonovich transport noise have unique local pathwise solutions.