On weighted estimates for the stream function of axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder

Abstract

Higher-order estimates in weighted Sobolev spaces for solutions to a singular elliptic equation for the stream function in an axially symmetric cylinder are provided. These estimates are essential for investigating the existence of axially symmetric solutions to incompressible Navier-Stokes equations in axially symmetric cylinders. To derive the estimates the technique of Kondratiev is incorporated. The weight has a form of a power function of the distance to the axis of symmetry