Decay estimates for homogeneous Boussinesq equations in a semi-infinite pipe

In this paper, we establish the spatial decay bounds for homogeneous Boussinesq equations in a semi-infinite pipe flow. Assuming that the entrance velocity and magnetic field data are restricted appropriately, and it converges to laminar flow as the distance down the pipe tends to infinity, we deriv...

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Bibliographic Details
Published in:Nonlinear analysis 2011-09, Vol.74 (13), p.4399-4417
Main Authors: Li, Yuanfei, Liu, Yan, Lin, Changhao
Format: Article
Language:English
Subjects:
Boussinesq equations
Decay
Decay bounds
Entrances
Estimates
Exact sciences and technology
Incompressible viscous fluid
Inequalities
Laminar flow
Magnetic fields
Mathematical analysis
Mathematics
Pipe
Saint-Venant principle
Sciences and techniques of general use
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Summary:In this paper, we establish the spatial decay bounds for homogeneous Boussinesq equations in a semi-infinite pipe flow. Assuming that the entrance velocity and magnetic field data are restricted appropriately, and it converges to laminar flow as the distance down the pipe tends to infinity, we derive a second order differential inequality that leads to an exponential decay estimate for the energy E ( z , t ) defined in (27). We also indicate how to establish the explicit bound for the total energy.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.03.062