EXISTENCE OF AXISYMMETRIC AND HOMOGENEOUS SOLUTIONS OF NAVIER-STOKES EQUATIONS IN CONE REGIONS

摘要

In this paper, we study axisymmetric homogeneous solutions ofthe Navier-Stokes equations in cone regions. In [James Serrin. The swirlingvortex. Philosophical Transactions of the Royal Society of London. Series A,Mathematical and Physical Sciences, 271(1214):325-360, 1972.], Serrin stud-ied the boundary value problem in half-space minus x3-axis, and used it tomodel the dynamics of tornado. We extend Serrin's work to general cone re-gions minus x3-axis. All axisymmetric homogeneous solutions of the boundaryvalue problem have three possible patterns, which can be classied by twoparameters. Some existence results are obtained as well.