On the existence of traveling waves in the 3D Boussinesq system

Details On the existence of traveling waves in the 3D Boussinesq system On the existence of traveling waves in the 3D Boussinesq system

2009-07-06

arxiv.org/abs/0907.1066v1

Mathematics

Analysis of PDEs

15 pages, to appear in Communications in Mathematical Physics

Scientific paper

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.

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