On the Existence of Traveling Waves in the 3D Boussinesq System |
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Authors: | Marta Lewicka and Piotr B Mucha |
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Institution: | 1.Department of Mathematics,University of Minnesota,Minneapolis,USA;2.Institute of Applied Mathematics and Mechanics,University of Warsaw,Warszawa,Poland |
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Abstract: | 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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Keywords: | |
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