Communications in Mathematical Physics

, Volume 259, Issue 2, pp 451-474

First online:

Traveling Fronts in a Reactive Boussinesq System: Bounds and Stability

  • Brandy WinnAffiliated withDepartment of Mathematics, University of Chicago Email author 

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This paper considers a simplified model of active combustion in a fluid flow, with the reaction influencing the flow. The model consists of a reaction-diffusion-advection equation coupled with an incompressible Navier-Stokes system under the Boussinesq approximation in an infinite vertical strip. We prove that for certain ignition nonlinearities, including all that are C 2, and for any domain width, planar traveling front solutions are nonlinearly and exponentially stable within certain weighted H 2 spaces, provided that the Rayleigh number ρ is small enough. The same result holds for bistable nonlinearities in unweighted H 2 spaces. We also obtain uniform bounds on the Nusselt number, the bulk burning rate, and the average maximum vertical velocity for chemistries that include bistable and ignition nonlinearities.