Abstract
For a prescribed deterministic kinetic energy, we use convex integration to construct analytically weak and probabilistically strong solutions to the 3D incompressible Navier–Stokes equations driven by a linear multiplicative stochastic forcing. These solutions are defined up to an arbitrarily large stopping time and have deterministic initial values, which are part of the construction. Moreover, by a suitable choice of different kinetic energies which coincide on an interval close to time 0, we obtain non-uniqueness.
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