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

Abstract

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.

Special Issue Editorial “Symmetry in the Mathematical Inequalities”

“…Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important. X. Chen et al, in the paper "Spatial Decay Bounds for the Brinkman Fluid Equations in Double-Diffusive Convection" [17], studied 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, the exponential decay estimates for homogeneous Brinkman equations are established.…”