Wydawnictwa / Banach Center Publications / Wszystkie tomy

Streszczenie

The existence and uniqueness of solutions to the Navier-Stokes equations in a cylinder $\Omega$ and with boundary slip conditions is proved. Assuming that the azimuthal derivative of cylindrical coordinates and azimuthal coordinate of the initial velocity and the external force are sufficiently small we prove long time existence of regular solutions such that the velocity belongs to $W_{5/2}^{2,1}(\Omega\times(0,T))$ and the gradient of the pressure to $L_{5/2}(\Omega\times(0,T))$. We prove the existence of solutions without any restrictions on the lengths of the initial velocity and the external force.