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. 407–437DOI 10.1016/J.ANIHPC.2004.10.010