Relaxation in reactive flows

Peter Constantin, Alexei Novikov, Lenya Ryzhik

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider convective systems in a bounded domain, in which viscous fluids described by the Stokes system are coupled using the Boussinesq approximation to a reaction-advection-diffusion equation for the temperature. We show that the resulting flows possess relaxation-enhancing properties in the sense of [CoKRZ]. In particular, we show that solutions of the nonlinear problems become small when gravity is sufficiently strong due to the improved interaction with the cold boundary. As an application, we deduce that the explosion threshold for power-like nonlinearities tends to infinity in the large Rayleigh number limit. We also discuss the behavior of the principal eigenvalues of the corresponding advection-diffusion problem and the quenching phenomenon for reaction-diffusion equations.

Original languageEnglish (US)
Pages (from-to)1145-1167
Number of pages23
JournalGeometric and Functional Analysis
Volume18
Issue number4
DOIs
Publication statusPublished - Dec 1 2008

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