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    Aristov, S.N. Privalova, V.V. and Prosviryakov, E. Y. 2016. Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer. Nelineinaya Dinamika, p. 167.


    Polyanin, Andrei D. and Zhurov, Alexei I. 2016. Functional and generalized separable solutions to unsteady Navier–Stokes equations. International Journal of Non-Linear Mechanics, Vol. 79, p. 88.


    Zeb, A. Siddiqui, A. M. and Ahmed, M. 2013. An Analysis of the Flow of a Newtonian Fluid between Two Moving Parallel Plates. ISRN Mathematical Analysis, Vol. 2013, p. 1.


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    2011. Handbook of Nonlinear Partial Differential Equations, Second Edition.


    Aristov, S. N. and Polyanin, A. D. 2010. New classes of exact solutions and some transformations of the Navier-Stokes equations. Russian Journal of Mathematical Physics, Vol. 17, Issue. 1, p. 1.


    Aristov, S. N. and Polyanin, A. D. 2009. Exact solutions of unsteady three-dimensional Navier-Stokes equations. Doklady Physics, Vol. 54, Issue. 7, p. 316.


    Aristov, S. N. Knyazev, D. V. and Polyanin, A. D. 2009. Exact solutions of the Navier-Stokes equations with the linear dependence of velocity components on two space variables. Theoretical Foundations of Chemical Engineering, Vol. 43, Issue. 5, p. 642.


    Polyanin, A. D. and Aristov, S. N. 2009. Systems of hydrodynamic type equations: Exact solutions, transformations, and nonlinear stability. Doklady Physics, Vol. 54, Issue. 9, p. 429.


    Polyanin, A. D. 2009. On the nonlinear instability of the solutions of hydrodynamic-type systems. JETP Letters, Vol. 90, Issue. 3, p. 217.


    Ke-Qin, Zhu Ling, Ren and Yi, Liu 2005. Linear Stability of Flows in a Squeeze Film. Chinese Physics Letters, Vol. 22, Issue. 6, p. 1460.


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  • Journal of Fluid Mechanics, Volume 464
  • August 2002, pp. 209-215

Viscous flow between two moving parallel disks: exact solutions and stability analysis

  • S. N. ARISTOV (a1) and I. M. GITMAN (a1) (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112002001003
  • Published online: 01 August 2002
Abstract

The motion of a viscous incompressible liquid between two parallel disks, moving towards each other or in opposite directions, is considered. The description of possible conditions of motion is based on the exact solution of the Navier–Stokes equations. Both stationary and transient cases have been considered. The stability of the motion is analysed for different initial perturbations. Different types of stability were found according to whether the disks moved towards or away from each other.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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