Global existence of solutions to Navier–Stokes equations in cylindrical domains
Volume 36 / 2009
Applicationes Mathematicae 36 (2009), 169-182
MSC: 35Q35, 76D03, 76D05.
DOI: 10.4064/am36-2-5
Abstract
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.
