Global existence and non-uniqueness for the Cauchy problem associated to 3D Navier–Stokes equations perturbed by transport noise Article Swipe

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Umberto Pappalettera ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1007/s40072-023-00318-5 · OA: W4388017540

We show global existence and non-uniqueness of probabilistically strong, analytically weak solutions of the three-dimensional Navier–Stokes equations perturbed by Stratonovich transport noise. We can prescribe either: (i) any divergence-free, square integrable intial condition; or (ii) the kinetic energy of solutions up to a stopping time, which can be chosen arbitrarily large with high probability. Solutions enjoy some Sobolev regularity in space but are not Leray–Hopf.