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

Abstract

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.

arXiv comment25 pages

References in corpus (9)

• Well-posedness of the transport equation by stochastic perturbation
• Dissipative continuous Euler flows
• Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations
• Degenerate parabolic stochastic partial differential equations: Quasilinear case
• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
• 2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction
• From additive to transport noise in 2D fluid dynamics
• Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
• Regularization by transport noise for 3D MHD equations