Local well-posedness for Boussinesq approximation with shear dependent viscosities in 3D

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• 作者：Changjia Wang ; ^{wangchangjia@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{wangchangjia@163.com" class="auth_mail" title="E-mail the corresponding author} ; Qun Dai
• 关键词：Weak solutions ; Boussinesq approximation ; Shear dependent viscosity
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：72
• 期：1
• 页码：131-146
• 全文大小：414 K

文摘

In this paper, we prove the existence and uniqueness of regular weak solutions for a nonlinear Boussinesq system in a small time interval. The viscosity is assumed to be with a p$p$-structure depending on the shear rate. We mainly work on 3D case with periodic boundary and initial value conditions. The W^2,p$W^{2,p}$-type regularity for velocity and H²$H^2$-type regularity for temperature were obtained for $\frac{7}{5}<p\le 2$.