No blow-up by nonlinear Itô noise for the Euler equations

Abstract

By employing a suitable multiplicative Itô noise with radial structure and with more than linear growth, we show the existence of a unique, global-in-time, strong solution for the stochastic Euler equations in two and three dimensions. More generally, we consider a class of stochastic partial differential equations (SPDEs) with a superlinear growth drift and suitable nonlinear, multiplicative Itô noise, with the stochastic Euler equations as a special case within this class. We prove that the addition of such a noise effectively prevents blow-ups in the solution of these SPDEs.

arXiv commentRevised version accepted in Electron. J. Probab

References in corpus (16)

• Well-posedness of the transport equation by stochastic perturbation
• SPDE in Hilbert Space with Locally Monotone Coefficients
• Local Martingale and Pathwise Solutions for an Abstract Fluids Model
• Strong illposedness of the incompressible Euler equation in integer $C^m$ spaces
• Noise Prevents Singularities in Linear Transport Equations
• Solution properties of a 3D stochastic Euler fluid equation
• Pathwise uniqueness and continuous dependence for SDEs with nonregular drift
• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
• Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity
• Blow-up for the stochastic nonlinear Schrodinger equation with multiplicative noise
• Stochastic Navier-Stokes Equations and Related Models
• Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
• Quantitative convergence rates for scaling limit of SPDEs with transport noise
• Absolute continuity under flows generated by SDE with measurable drift coefficient
• Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise
• Non-explosion by Stratonovich noise for ODEs