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.
2021-01-01

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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