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

Galeati L.;
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.
File in questo prodotto:
File Dimensione Formato  
Flandoli Galeati Luo delayed blow up.pdf

solo utenti autorizzati

Licenza: Creative commons
Dimensione 341.86 kB
Formato Adobe PDF
341.86 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/244639
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 31
social impact