1 research outputs found
On the existence of traveling waves in the 3D Boussinesq system
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.Comment: 15 pages, to appear in Communications in Mathematical Physic