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

Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk 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 $$\left\| F\right\| _{BMO}^{2}$$ F B M O 2 , $$\left\| g\right\| _{BMO}^{2}$$ g B M O 2 , $$\left\| \frac{\partial g}{\partial y}\right\| _{BMO}^{2}$$ ∂ g ∂ y B M O 2 and $$\left\| \frac{\partial ^{2} g}{\partial y^{2}}\right\| _{BMO}^{2}$$ ∂ 2 g ∂ y 2 B M O 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 $$g=\nabla \times F=\frac{\partial F}{\partial z}$$ g = ∇ × F = ∂ F ∂ z is the vorticity of the rotating fluid. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

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

, Volume 7 (1) – Apr 6, 2016
13 pages

Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-016-0132-x
Publisher site
See Article on Publisher Site

### Abstract

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 $$\left\| F\right\| _{BMO}^{2}$$ F B M O 2 , $$\left\| g\right\| _{BMO}^{2}$$ g B M O 2 , $$\left\| \frac{\partial g}{\partial y}\right\| _{BMO}^{2}$$ ∂ g ∂ y B M O 2 and $$\left\| \frac{\partial ^{2} g}{\partial y^{2}}\right\| _{BMO}^{2}$$ ∂ 2 g ∂ y 2 B M O 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 $$g=\nabla \times F=\frac{\partial F}{\partial z}$$ g = ∇ × F = ∂ F ∂ z is the vorticity of the rotating fluid.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Apr 6, 2016