A stationary solution to the air motion equations in the lower part of a typhoon

The existence of a stationary axisymmetric solution is proved to the model equations describing the air motion in the lower part of a typhoon. These are the equations (averaged over the vertical component) of motion of a barotropic viscous gas with constant coefficients of the dynamic and volume viscosities, under the conditions of a constant external friction, the Coriolis force, and the mass outflow from the central part. It is required that the components of the solution at infinity be continuous and decrease to zero at infinity. It is shown that, for the existence of a nontrivial solution of this type, it is necessary that the Coriolis parameter be nonzero and that there be a mass outflow small as compared to the coefficients of the external friction and viscosity.