scholarly journals Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow

2016 ◽  
Vol 36 (10) ◽  
pp. 5369-5386 ◽  
Author(s):  
Changjie Fang ◽  
Weimin Han
Keyword(s):  
Optimal Control ◽  
Fluid Flow ◽  
Hemivariational Inequality ◽  
Well Posedness ◽  
Stokes Fluid

On the Cauchy problem associated with the Brinkman flow in

2021 ◽  
pp. 1-20
Author(s):  
Michel Molina Del Sol ◽  
Eduardo Arbieto Alarcon ◽  
Rafael José Iorio
Keyword(s):  
Cauchy Problem ◽  
Porous Media ◽  
Fluid Flow ◽  
Comparison Principle ◽  
Well Posedness ◽  
Quasilinear Equations ◽  
Brinkman Equations ◽  
The Cauchy Problem ◽  
Model Fluid ◽  
Image Position

In this study, we continue our study of the Cauchy problem associated with the Brinkman equations [see (1.1) and (1.2) below] which model fluid flow in certain types of porous media. Here, we will consider the flow in the upper half-space \[ \mathbb{R}_{+}^{3}=\left\{\left(x,y,z\right) \in\mathbb{R}^{3}\left\vert z\geqslant 0\right.\right\}, \] under the assumption that the plane $z=0$ is impenetrable to the fluid. This means that we will have to introduce boundary conditions that must be attached to the Brinkman equations. We study local and global well-posedness in appropriate Sobolev spaces introduced below, using Kato's theory for quasilinear equations, parabolic regularization and a comparison principle for the solutions of the problem.

scholarly journals Control of mixing in a Stokes’ fluid flow

2010 ◽  
Vol 20 (10) ◽  
pp. 1103-1115 ◽  
Author(s):  
Ian J. Couchman ◽  
Eric C. Kerrigan
Keyword(s):  
Fluid Flow ◽  
Stokes Fluid
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