Global Weak Solutions To The Navier{Stokes{Darcy{Boussinesq System For Thermal Convection In Coupled Free And Porous Media Flows
Abstract
We study the Navier{Stokes{Darcy{Boussinesq system that models the thermal convection of a uid 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.
Recommended Citation
X. Wang and H. Wu, "Global Weak Solutions To The Navier{Stokes{Darcy{Boussinesq System For Thermal Convection In Coupled Free And Porous Media Flows," Advances in Differential Equations, vol. 26, no. 1 thru 2, pp. 1 - 44, Project Euclid, Jan 2021.
The definitive version is available at https://doi.org/10.57262/ade/1610420433
International Standard Serial Number (ISSN)
1079-9389
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Project Euclid, All rights reserved.
Publication Date
01 Jan 2021
Comments
National Natural Science Foundation of China, Grant 11871159