Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk

详细信息    查看全文

• 作者：S. Rahman ; T. Hayat ; B. Ahmad
• 关键词：Rotating frame ; Third grade fluid ; MHD equations ; Regularity criteria
• 刊名：Analysis and Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：7
• 期：1
• 页码：93-105
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1664-235X
• 卷排序：7

文摘

The purpose of present paper is to establish the regularity criteria for nonlinear problem of unsteady flow of third grade fluid in a rotating frame. The fluid is between two plates and the lower plate is porous. The main result of this paper is to establish the global regularity of classical solutions when \(\left\| F\right\| _{BMO}^{2}\), \(\left\| g\right\| _{BMO}^{2}\), \(\left\| \frac{\partial g}{\partial y}\right\| _{BMO}^{2}\) and \(\left\| \frac{\partial ^{2} g}{\partial y^{2}}\right\| _{BMO}^{2}\) are sufficiently small. In addition uniqueness of weak solution is also verified. Here BMO denotes the homogeneous space of bounded mean oscillations, F is the velocity and \(g=\nabla \times F=\frac{\partial F}{\partial z}\) is the vorticity of the rotating fluid.