Delayed blow-up by transport noise

Abstract

For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed by multiplicative noise of transport type in a certain scaling limit. The main result is applied to the 3D Keller-Segel, 3D Fisher-KPP and 2D Kuramoto-Sivashinsky equations, yielding long-time existence for large initial data with high probability.

arXiv comment30 pages

References in corpus (4)

• Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions
• On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
• Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system
• Global existence for the two-dimensional Kuramoto-Sivashinsky equation with advection