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

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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 \(\left\| F\right\| _{BMO}^{2}\), \(\left\| g\right\| _{BMO}^{2}\), \(\left\| \frac{\partial g}{\partial y}\right\| _{BMO}^{2}\) 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.

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Acknowledgments

The author would like to express sincere gratitude to Professor Pengcheng Niu for guidance, constant encouragement and providing an excellent research environment.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

    S. Rahman

  2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710129, Shaanxi, People’s Republic of China

    S. Rahman

  3. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & B. Ahmad

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  1. S. Rahman
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Correspondence to S. Rahman.

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Rahman, S., Hayat, T. & Ahmad, B. Regularity criteria for unsteady MHD third grade fluid due to rotating porous disk. Anal.Math.Phys. 7, 93–105 (2017). https://doi.org/10.1007/s13324-016-0132-x

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  • DOI: https://doi.org/10.1007/s13324-016-0132-x

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