### Global special regular solutions to the Navier-Stokes equations in a cylindrical domain without the axis of symmetry

DOI: http://dx.doi.org/10.12775/TMNA.2004.020

#### Abstract

Global existence of regular solutions to the Navier-Stokes equations in

a bounded cylindrical domain without the axis of symmetry and with boundary

slip conditions is proved. We showed the existence of solutions without

restrictions on the magnitude of the initial velocity assuming only that the

$L_2$-norms of the angular derivative of the cylindrical components of the

initial velocity and the external force are sufficiently small.

To prove global existence some decay estimates on the external force are

imposed.

a bounded cylindrical domain without the axis of symmetry and with boundary

slip conditions is proved. We showed the existence of solutions without

restrictions on the magnitude of the initial velocity assuming only that the

$L_2$-norms of the angular derivative of the cylindrical components of the

initial velocity and the external force are sufficiently small.

To prove global existence some decay estimates on the external force are

imposed.

#### Keywords

Navier-Stokes equations; initial-boundary value problem; global existence; regularity; large data

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