The explosion problem in a flow

Henri Berestycki, Alexander Kiselev, Alexei Novikov, Lenya Ryzhik

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)31-65
Number of pages35
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Jan 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)


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