Some solutions of continuum equations for an incompressible viscous medium

Abstract

We consider the Navier-Stokes equations for an incompressible medium that fills at any time t ? 0 an open axially symmetric cylindric layer D. We find solutions of these equations in the class of motions described by velocity fields whose lines for t ? 0 coincide with their vortex lines and lie on axially symmetric cylindrical surfaces in D. © 2014, Pleiades Publishing, Ltd.