Well-posedness and Regularity of the Darcy-Boussinesq System in Layered Porous Media
Abstract
We establish the existence of global weak solution in 2D and 3D, as well as the uniqueness of weak solution in 2D, for the Darcy-Boussinesq model for convection in layered porous media with square integrable initial data. We also derive tangential regularity in the 2D case. In addition, we obtain the existence and uniqueness of regular solution in a novel piecewise H2 space in both 2D and 3D under uniform porosity assumption and H1 initial data. This is the first rigorous result for this model in the physically important layered setting.
Recommended Citation
Y. Cao et al., "Well-posedness and Regularity of the Darcy-Boussinesq System in Layered Porous Media," Discrete and Continuous Dynamical Systems Series B, vol. 30, no. 12, pp. 4764 - 4783, American Institute of Mathematical Sciences, Dec 2025.
The definitive version is available at https://doi.org/10.3934/dcdsb.2025083
Department(s)
Mathematics and Statistics
Keywords and Phrases
Darcy-Boussinesq System; Layered Porous Media; Regularity; Well-posedness
International Standard Serial Number (ISSN)
1531-3492
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 American Institute of Mathematical Sciences, All rights reserved.
Publication Date
01 Dec 2025
Comments
National Natural Science Foundation of China, Grant 12371106