论文标题
Navier-Stokes-Darcy-BoussinesQ系统用于热对流的全球弱解决方案，耦合免费和多孔介质流动
Global Weak Solutions to the Navier-Stokes-Darcy-Boussinesq System for Thermal Convection in Coupled Free and Porous Media Flows
论文作者
论文摘要
我们研究了Navier-Stokes-Darcy-BoussinesQ系统，该系统模拟了一般分解域中覆盖饱和多孔培养基的流体的热对流。在两个和三个空间维度中，我们首先证明了由狮子和海狸 - 约瑟夫·塞夫曼·琼斯的界面条件下的初始边界价值问题的全局弱解。证明是基于适当的时间限制的离散化计划，并结合了Leray-Schauder原理和紧凑性论证。接下来，我们建立一个弱的唯一性结果，使得弱解决方案与从相同初始数据产生的强溶液一致，只要后者存在。
We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of global weak solutions to the initial boundary value problem subject to the Lions and Beavers-Joseph-Saffman-Jones interface conditions. The proof is based on a proper time-implicit discretization scheme combined with the Leray-Schauder principle and compactness arguments. Next, we establish a weak-strong uniqueness result such that a weak solution coincides with a strong solution emanating from the same initial data as long as the latter exists.
