Geodesic
Global attractor for Navier–Stokes equations in cylindrical domains
Bernard Nowakowski 1   ; Wojciech M. Zaj/aczkowski 2
1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland
2 Institute 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
Applicationes Mathematicae, Tome 36 (2009) no. 2, pp. 183-194 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am36-2-6
Keywords: global regular solutions navier stokes system cylindrical domains have already obtained under assumption smallness derivative velocity field respect variable along axis cylinder derivative force field respect variable along axis cylinder projection force field axis cylinder restricted part boundary perpendicular axis cylinder assumptions prove paper existence global attractor navier stokes equations convergence solutions stationary solutions large viscosity coefficient

Bernard Nowakowski  1   ; Wojciech M. Zaj/aczkowski  2

1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland
2 Institute 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 
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     author = {Bernard Nowakowski and Wojciech M. Zaj/aczkowski},
     title = {Global attractor for {Navier{\textendash}Stokes} equations
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     journal = {Applicationes Mathematicae},
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 in cylindrical domains
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Bernard Nowakowski; Wojciech M. Zaj/aczkowski. Global attractor for Navier–Stokes equations
 in cylindrical domains. Applicationes Mathematicae, Tome 36 (2009) no. 2, pp. 183-194. doi: 10.4064/am36-2-6

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