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

Wojciech M. Zajączkowski

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.

Keywords


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

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