The explosion problem in a flow

Henri Berestycki; Alexander Kiselev; Alexei Novikov; Lenya Ryzhik

doi:10.1007/s11854-010-0002-7

The explosion problem in a flow

Henri Berestycki, Alexander Kiselev, Alexei Novikov, Lenya Ryzhik

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We consider the explosion problem in an incompressible flow introduced in [5]. We use a novel L^p - L^∞ estimate for elliptic advection-diffusion problems to show that the explosion threshold obeys a positive lower bound which is uniform in the advecting flow. We also identify the flows for which the explosion threshold tends to infinity as their amplitude grows and obtain an effective description of the explosion threshold in the strong flow asymptotics in two-dimensional cellular flows.

Original language	English (US)
Pages (from-to)	31-65
Number of pages	35
Journal	Journal d'Analyse Mathematique
Volume	110
Issue number	1
DOIs	https://doi.org/10.1007/s11854-010-0002-7
State	Published - Jan 2010

All Science Journal Classification (ASJC) codes

Analysis
Mathematics(all)

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10.1007/s11854-010-0002-7

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abstract = "We consider the explosion problem in an incompressible flow introduced in [5]. We use a novel Lp - L∞ estimate for elliptic advection-diffusion problems to show that the explosion threshold obeys a positive lower bound which is uniform in the advecting flow. We also identify the flows for which the explosion threshold tends to infinity as their amplitude grows and obtain an effective description of the explosion threshold in the strong flow asymptotics in two-dimensional cellular flows.",

author = "Henri Berestycki and Alexander Kiselev and Alexei Novikov and Lenya Ryzhik",

note = "Funding Information: Acknowledgment. This work was carried out when the first author was visiting the University of Chicago. It was supported by the ASC Flash Center at the University of Chicago. AK was supported by NSF grant DMS-0314129, AN by NSF grant DMS-0604600 and LR by NSF grant DMS-0604687.",

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AB - We consider the explosion problem in an incompressible flow introduced in [5]. We use a novel Lp - L∞ estimate for elliptic advection-diffusion problems to show that the explosion threshold obeys a positive lower bound which is uniform in the advecting flow. We also identify the flows for which the explosion threshold tends to infinity as their amplitude grows and obtain an effective description of the explosion threshold in the strong flow asymptotics in two-dimensional cellular flows.

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The explosion problem in a flow

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