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.
Analysis and Mathematical Physics – Springer Journals
Published: Apr 6, 2016
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