Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman-Oberbeck-Boussinesq System
Abstract
In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial-boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.
Recommended Citation
M. Fei et al., "Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman-Oberbeck-Boussinesq System," Physica D: Nonlinear Phenomena, vol. 338, pp. 42 - 56, Elsevier, Jan 2017.
The definitive version is available at https://doi.org/10.1016/j.physd.2016.08.002
Department(s)
Mathematics and Statistics
Keywords and Phrases
Physics; Approximate solution; Boussinesq system; Darcy equations; Darcy number; Initial layer; Method of multiple scale; Optimal convergence; Singular perturbation problems; Boundary layers; Boundary layer; Darcy-Brinkman-Oberbeck-Boussinesq system; Initial layer; Initial-boundary layer; Vanishing Darcy number limit
International Standard Serial Number (ISSN)
0167-2789
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2017 Elsevier, All rights reserved.
Publication Date
01 Jan 2017
Comments
This work was completed during the first author's visit to the Florida State University. He is grateful for the hospitality of the math department. First author was supported by NSFC grant 11301005 , CSC grant 201508340024 and AHNSF grant 1608085MA13 . Third author was supported by NSF grant DMS-1312701.