Global existence and non-uniqueness for the Cauchy problem associated to 3D Navier-Stokes equations perturbed by transport noise
| Autor: | Pappalettera, Umberto |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Stoch. Partial Differ. Equ. Anal. Comput. (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40072-023-00318-5 |
| Popis: | 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: \emph{i}) any divergence-free, square integrable intial condition; or \emph{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. Comment: 25 pages |
| Databáze: | arXiv |
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