Large time regular solutions to the Navier-Stokes equations in cylindrical domains

Joanna Rencławowicz, Wojciech M. Zajączkowski

DOI: http://dx.doi.org/10.12775/TMNA.2008.036

Abstract


We prove the large time existence of solutions to the
Navier-Stokes equations with slip boundary conditions in a
cylindrical domain. Assuming smallness of $L_2$-norms of
derivatives of initial velocity with respect to variable along the
axis of the cylinder, we are able to obtain estimate for velocity
in $W^{2,1}_2$ without restriction on its magnitude. Then
existence follows from the Leray-Schauder fixed point theorem.

Keywords


Navier-Stokes equations; motions in cylindrical domains; boundary slip conditions; global existence of regular solutions; large data

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