Geodesic
On weighted estimates for the stream function of axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder
Bernard Nowakowski1 ; Wojciech M. Zajączkowski2
1 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology 00-908 Warszawa, Poland <a href="https://orcid.org/0000-0002-5142-7827">ORCID: 0000-0002-5142-7827</a>
2 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology 00-908 Warszawa, Poland and Institute of Mathematics Polish Academy of Sciences 00-656 Warszawa, Poland
Applicationes Mathematicae, Tome 50 (2023) no. 2, pp. 123-148.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 the proof of the global existence of regular axially symmetric solutions to incompressible Navier–Stokes equations in axially symmetric cylinders. In order to derive the estimates, the technique of weighted Sobolev spaces developed by Kondrat’ev is applied. The weight is a power function of the distance to the axis of symmetry.
DOI : 10.4064/am2488-1-2024
Keywords: higher order estimates weighted sobolev spaces solutions singular elliptic equation stream function axially symmetric cylinder provided these estimates essential proof global existence regular axially symmetric solutions incompressible navier stokes equations axially symmetric cylinders order derive estimates technique weighted sobolev spaces developed kondrat applied weight power function distance axis symmetry

Bernard Nowakowski 1 ; Wojciech M. Zajączkowski 2

1 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology 00-908 Warszawa, Poland <a href="https://orcid.org/0000-0002-5142-7827">ORCID: 0000-0002-5142-7827</a>
2 Institute of Mathematics and Cryptology Cybernetics Faculty Military University of Technology 00-908 Warszawa, Poland and Institute of Mathematics Polish Academy of Sciences 00-656 Warszawa, Poland 
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Bernard Nowakowski; Wojciech M. Zajączkowski. On weighted estimates for the stream function of axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder. Applicationes Mathematicae, Tome 50 (2023) no. 2, pp. 123-148. doi : 10.4064/am2488-1-2024. http://geodesic.mathdoc.fr/articles/10.4064/am2488-1-2024/

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