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.

Delayed blow-up by transport noise

Flandoli F.;Galeati L.;Luo D.
2021

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.
2021
Settore MAT/06 - Probabilita' e Statistica Matematica
60H15; 60H50; Dissipation enhancement; Fisher–KPP equation; Keller–Segel equation; Kuramoto–Sivashinsky equation; scaling limit; transport noise
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/110170
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