Global attractor for Navier–Stokes equations in cylindrical domains

Tom 36 / 2009

Bernard Nowakowski, Wojciech M. Zaj/aczkowski Applicationes Mathematicae 36 (2009), 183-194 MSC: 34D05, 34D45, 35Q30, 76D03, 76D05. DOI: 10.4064/am36-2-6

Streszczenie

Global and regular solutions of the Navier–Stokes system in cylindrical domains have already been obtained under the assumption of smallness of $(1)$ the derivative of the velocity field with respect to the variable along the axis of cylinder, $(2)$ the derivative of force field with respect to the variable along the axis of the cylinder and $(3)$ the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder. With the same assumptions we prove in this paper the existence of a global attractor for the Navier–Stokes equations and convergence of solutions to the stationary solutions for the large viscosity coefficient.

Autorzy

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

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