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arXiv · 2210.15729

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

Bernard Nowakowski·Wojciech Zajączkowski
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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.

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Bernard Nowakowski, Wojciech Zajączkowski. 2023-04-02. On weighted estimates for the stream function of axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder. https://arxiv.org/abs/2210.15729

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