On some classes of nonstationary axially symmetric solutions to the NavierStokes equations
Abstract
In the paper, the NavierStokes equations are studied in axially symmetric cases of nonstationary motion with rotation of incompressible viscous fluids. The problem is reduced to a nonlinear system of three partial differential equations for three unknown functions of the cylindrical coordinates r and z and time t. The three functions are sought in the form of power series in r with coefficients depending on t and z. For the unknown coefficients recurrence relations are obtained which contain three arbitrary functions. The relations are examined in three particular cases in which they give analytical solutions to the NavierStokes equations for any values of the coordinates t, z, and r.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 September 2014
 DOI:
 10.1063/1.4895463
 Bibcode:
 2014JMP....55i3102R