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.
Citation
Joanna Rencławowicz. Wojciech M. Zajączkowski. "Large time regular solutions to the Navier-Stokes equations in cylindrical domains." Topol. Methods Nonlinear Anal. 32 (1) 69 - 87, 2008.
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