Global existence of solutions to Navier–Stokes equations in cylindrical domains

Volume 36 / 2009

Bernard Nowakowski, Wojciech M. Zaj/aczkowski Applicationes Mathematicae 36 (2009), 169-182 MSC: 35Q35, 76D03, 76D05. DOI: 10.4064/am36-2-5


We prove the existence of global and regular solutions to the Navier–Stokes equations in cylindrical type domains under boundary slip conditions, where coordinates are chosen so that the $x_3$-axis is parallel to the axis of the cylinder. Regular solutions have already been obtained on the interval $[0,T]$, where $T>0$ is large, on the assumption that the $L_2$-norms of the third component of the force field, of derivatives of the force field, and of the velocity field with respect to the direction of the axis of the cylinder are small. In this paper we continue the solution to all times.


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

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