Geodesic
Global existence of solutions to Navier–Stokes equations in cylindrical domains
Bernard Nowakowski1 ; Wojciech M. Zaj/aczkowski2
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. 169-182 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am36-2-5
Keywords: prove existence global regular solutions navier stokes equations cylindrical type domains under boundary slip conditions where coordinates chosen axis parallel axis cylinder regular solutions have already obtained interval where large assumption norms third component force field derivatives force field velocity field respect direction axis cylinder small paper continue solution times

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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     title = {Global existence of solutions to
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     journal = {Applicationes Mathematicae},
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Bernard Nowakowski; Wojciech M. Zaj/aczkowski. Global existence of solutions to
 Navier–Stokes equations in
 cylindrical domains. Applicationes Mathematicae, Tome 36 (2009) no. 2, pp. 169-182. doi: 10.4064/am36-2-5

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