Solvability of the Poisson equation in weighted Sobolev spaces

Volume 37 / 2010

Wojciech M. Zaj/aczkowski Applicationes Mathematicae 37 (2010), 325-339 MSC: 35K05, 35K20. DOI: 10.4064/am37-3-4

Abstract

The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier–Stokes equations which are close to axially symmetric solutions.

Authors

  • Wojciech M. Zaj/aczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    and
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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