论文标题
多孔媒体中三维的三维Brinkman-Forchheimer-Bénard对流模型的全球良好性
Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media
论文作者
论文摘要
我们认为在多孔培养基的封闭样品中，不可压缩流体的三维（3D）Boussinesq对流系统。具体而言，我们介绍和分析了3D Brinkman-Forchheimer-Bénard对流问题，描述了从底部加热并从顶部冷却的两个板之间的多孔介质中不可压缩的液体的行为。我们显示了全球及时解决方案的存在和独特性，以及在$ l^2 $和$ h^1 $中吸收球的存在。最终，我们对数据同化算法的适用性发表评论。
We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-Bénard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in $L^2$ and $H^1$. Eventually, we comment on the applicability of a data assimilation algorithm to our system.
