Delayed blow-up by transport noise

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...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 46; no. 9; pp. 1757 - 1788
Main Authors Flandoli, Franco, Galeati, Lucio, Luo, Dejun
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.09.2021
Taylor & Francis Ltd
Subjects
Dissipation enhancement
Fisher-KPP equation
Keller-Segel equation
Kuramoto-Sivashinsky equation
scaling limit
Toruses
transport noise
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2021.1893748