LAUSR

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 $$\left\| F\right\| _{BMO}^{2}$$FBMO2, $$\left\| g\right\| _{BMO}^{2}$$gBMO2, $$\left\| \frac{\partial g}{\partial y}\right\| _{BMO}^{2}$$∂g∂yBMO2 and $$\left\| \frac{\partial ^{2} g}{\partial y^{2}}\right\| _{BMO}^{2}$$∂2g∂y2BMO2 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.