Existence of solutions to the nonstationary Stokes system in $H_{-\mu}^{2,1}$, $\mu\in (0,1)$, in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

Volume 34 / 2007

W. M. Zaj/aczkowski Applicationes Mathematicae 34 (2007), 121-141 MSC: 35Q30, 76D03, 76D07, 76D99. DOI: 10.4064/am34-2-1


We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the second, we show an estimate in 3d in weighted spaces near the axis. Finally, in the third, the existence in a bounded domain is proved. This paper contains the first part of the proof


  • W. M. Zaj/aczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-956 Warszawa, Poland
    Institute of Mathematics and Cryptology
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland

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