Initial-boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system

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• 作者：Mingwen Fei^a ; ^{ahnufmwen@126.com" class="auth_mail" title="E-mail the corresponding author} ; Daozhi Han^b ; ^{djhan@iu.edu" class="auth_mail" title="E-mail the corresponding author} ; Xiaoming Wang^c ; ^{wxm@math.fsu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Initial layer ; Boundary layer ; Initial&ndash ; boundary layer ; Vanishing Darcy number limit ; Darcy&ndash ; Brinkman&ndash ; Oberbeck&ndash ; Boussinesq system ; Darcy equation
• 刊名：Physica D: Nonlinear Phenomena
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：338
• 期：Complete
• 页码：42-56
• 全文大小：547 K

文摘

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.