Spatial Decay for Solutions to 2-D Boussinesq System with Variable Thermal Diffusivity

In this paper, the authors derive an explicit spatial decay estimate for the time dependent flow of Boussinesq fluid with thermal conductivity depending on the temperature in a semi-infinite strip. By introducing a stream function, the authors established a decay estimate for an expression involving...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2018-04, Vol.154 (1), p.111-130
Main Authors: Li, Yuanfei, Lin, Changhao
Format: Article
Language:English
Subjects:
Applications of Mathematics
Boundary conditions
Boussinesq equations
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Decay
Estimates
Inverse problems
Mathematics
Mathematics and Statistics
Partial Differential Equations
Probability Theory and Stochastic Processes
Stream functions (fluids)
Thermal conductivity
Thermal diffusivity
Viscosity
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Summary:In this paper, the authors derive an explicit spatial decay estimate for the time dependent flow of Boussinesq fluid with thermal conductivity depending on the temperature in a semi-infinite strip. By introducing a stream function, the authors established a decay estimate for an expression involving the stream function. To make the result explicit, an upper bound for total energy is also obtained. The results of this paper may be thought of as a version of Saint-Venant’s principle.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-017-0136-z