tailieunhanh - Global regularity for unsteady flow of third grade fluid in an annular region

This article develops global regularity criteria for unsteady and magnetohydrodynamic flow of third grade fluid in terms of bounded mean oscillations. Uniqueness of the solution is also verified. | Turk J Math (2016) 40: 728 – 739 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Global regularity for unsteady flow of third grade fluid in an annular region Saeed ur RAHMAN1,∗, Tasawar HAYAT2,3 , Hamed H. ALSULAMI3 Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan 2 Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan 3 Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia 1 Received: • Accepted/Published Online: • Final Version: Abstract: This article develops global regularity criteria for unsteady and magnetohydrodynamic flow of third grade fluid in terms of bounded mean oscillations. Uniqueness of the solution is also verified. Key words: Nonlinear problem, global regularity, third grade fluid, annular pipe, magnetohydrodynamic flow 1. Introduction Non-Newtonian materials are now well recognized by scientists and engineers due to their industrial and technological applications. Several biological liquids also exhibit the rheological characteristics of non-Newtonian materials. Such materials having a magnetohydrodynamic character play a pivotal role in polymer processing, treatment of hyperthermia, cancer therapy, and many other fields. It is, however, well known that the flow of non-Newtonian fluids cannot be addressed by using the classical Navier–Stokes equations. This is because of their viscoelastic features in addition to the viscosity. Different non-Newtonian fluids have distinct rheological properties. Hence, several constitutive equations have been recommended for the flow analysis of non-Newtonian materials. The non-Newtonian fluids in general are classified into differential, rate, and integral categories. Several investigators in the field have chosen the simplest subclass of second grade fluid. .