论文标题
在通道中多相流体的边界稳定执行器
Boundary stabilizing actuators for multi-phase fluids in a channel
论文作者
论文摘要
这项工作致力于在三维通道样域$（x，x，y，z）\ in \ mathbb {r} \ times（0,1）\ times \ times \ mathbb {r} $中，将两种粘性和不可压缩流体的混合物边界稳定问题。该模型由Navier-Stokes方程组成，管理流体速度，并与对流的Cahn-Hilliard方程相结合，用于其中一种流体的原子的相对密度。我们在这里设计的反馈控制器仅在两个墙壁上的速度字段的切向组件上进行驱动$ y = 0,1 $。此外，它以简单明了的形式给出，从计算的角度易于操纵。无论混合物的运动学粘度多大，稳定性都可以保证。它也独立于系统的其他系数。
This work is devoted to the problem of boundary stabilization of a mixture of two viscous and incompressible fluids in a three dimensional channel-like domain $(x,y,z)\in \mathbb{R}\times (0,1)\times\mathbb{R}$. The model consists of the Navier-Stokes equations, governing the fluid velocity, coupled with a convective Cahn-Hilliard equation for the relative density of the atoms of one of the fluids. The feedback controller, we design here, is with actuation only on the tangential component of the velocity field on both walls $y=0,1$. Moreover, it is given in a simple and explicit form, easy to manipulate from the computational point of view. The stability is guaranteed no matter how large the kinematic viscosity of the mixture is. Also it is independent of the other coefficients of the system.
