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

Tom 50 / 2023

Bernard Nowakowski, Wojciech M. Zajączkowski Applicationes Mathematicae 50 (2023), 123-148 MSC: Primary 35J15; Secondary 35J75, 35Q30, 76D05 DOI: 10.4064/am2488-1-2024 Opublikowany online: 29 January 2024

Streszczenie

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.

Autorzy

  • Bernard NowakowskiInstitute of Mathematics and Cryptology
    Cybernetics Faculty Military University of Technology
    00-908 Warszawa, Poland
    ORCID: 0000-0002-5142-7827
    e-mail
  • Wojciech M. ZajączkowskiInstitute 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
    e-mail

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