JournalsaihpcVol. 23, No. 4pp. 407–437

Non-planar fronts in Boussinesq reactive flows

  • Henri Berestycki

    EHESS, CAMS, 54, boulevard Raspail, 75006 Paris, France
  • Peter Constantin

    Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
  • Lenya Ryzhik

    Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
Non-planar fronts in Boussinesq reactive flows cover
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Abstract

We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.

Cite this article

Henri Berestycki, Peter Constantin, Lenya Ryzhik, Non-planar fronts in Boussinesq reactive flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 4, pp. 407–437

DOI 10.1016/J.ANIHPC.2004.10.010