scholarly journals Spatial decay bounds for the channel flow of the Boussinesq equations

2011 ◽  
Vol 381 (1) ◽  
pp. 87-109 ◽  
Author(s):  
Yan Liu ◽  
Yuanfei Li ◽  
Yiwu Lin ◽  
Zhengan Yao
Keyword(s):  
Channel Flow ◽  
Boussinesq Equations ◽  
Spatial Decay ◽  
Decay Bounds

SPATIAL DECAY BOUNDS IN THE CHANNEL FLOW OF AN INCOMPRESSIBLE VISCOUS FLUID

2004 ◽  
Vol 14 (06) ◽  
pp. 795-818 ◽  
Author(s):  
CHANGHAO LIN ◽  
LAWRENCE E. PAYNE
Keyword(s):  
Laminar Flow ◽  
Viscous Fluid ◽  
Channel Flow ◽  
Exponential Decay ◽  
Transient Flow ◽  
Incompressible Viscous Fluid ◽  
Spatial Decay ◽  
Decay Bounds ◽  
Channel Boundary ◽  
Entrance Velocity

In this paper, we study the transient flow of an incompressible viscous fluid in a semi-infinite channel assuming adherence at the channel boundary. We show that under appropriate restrictions on the data if the fluid is initially at rest and the channel entrance velocity and/or channel width are sufficiently small, the solution will tend exponentially to a transient laminar flow as the distance form the entry section tends to infinity. In fact explicit exponential decay bounds are obtained.

scholarly journals Spatial Decay Bounds for the Brinkman Fluid Equations in Double-Diffusive Convection

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 98
Author(s):  
Xuejiao Chen ◽  
Yuanfei Li ◽  
Dandan Li
Keyword(s):  
Pipe Flow ◽  
Nonlinear Boundary ◽  
Energy Analysis ◽  
Nonlinear Boundary Conditions ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Brinkman Equations ◽  
Diffusive Convection ◽  
Decay Bounds ◽  
Double Diffusive

In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, we establish the exponential decay estimates for homogeneous Brinkman equations. That is to prove that the solutions of the equation decay exponentially with the distance from the finite end of the cylinder. To make the estimate of decay explicit, the bound for the total energy is also derived.

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