Well-posedness and regularity of the Darcy-Boussinesq system in layered porous media

2023/10/23 by Yining Cao, Cao, Yining, Weisheng Niu +3 · 1 citation
Engineering · Mathematics · #35Q35 #76E06 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2310.15088

openalex publication_date 2023/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 derived 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.

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• Vanishing layer thickness limit of convection in multilayer porous media

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