On axially symmetric solutions of the Navier-Stokes equations

  • Authors

    • Alexander S. Rabinowitch Department of Applied Mathematics, Mosow State University of Instrument Engineering and Computer Science, Moscow, Russia
    https://doi.org/10.14419/ijams.v1i4.1525
  • Axial rotation of fluids, differential rotation of stars and gas giants, incompressible viscous fluids, Navier-Stokes equations, solutions to Navier-Stokes equations.

  • Abstract

    In the present paper, the Navier-Stokes equations are studied in several axially symmetric cases. In them incompressible viscous fluids rotate about their axes and can change their shape. In the considered cases, three exact solutions to the Navier-Stokes equations are found. The first of these solutions describes rotating viscous fluids that are gradually cooling. The second of them describes nonstationary rotations with axial motions of viscous fluids. The third of the obtained solutions to the Navier-Stokes equations concerns rotating viscous fluids with stationary velocities. It is used to describe the observable phenomenon of differential rotation of the visible surfaces of stars and giant gas planets.

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  • How to Cite

    Rabinowitch, A. S. (2013). On axially symmetric solutions of the Navier-Stokes equations. International Journal of Advanced Mathematical Sciences, 1(4), 199-206. https://doi.org/10.14419/ijams.v1i4.1525