TY - JOUR AU - Rencławowicz, Joanna AU - Zajączkowski, Wojciech M. PY - 2008/09/01 Y2 - 2024/03/29 TI - Large time regular solutions to the Navier-Stokes equations in cylindrical domains JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 32 IS - 1 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2008.036 SP - 69 - 87 AB - We prove the large time existence of solutions to theNavier-Stokes equations with slip boundary conditions in acylindrical domain. Assuming smallness of $L_2$-norms ofderivatives of initial velocity with respect to variable along theaxis of the cylinder, we are able to obtain estimate for velocityin $W^{2,1}_2$ without restriction on its magnitude. Thenexistence follows from the Leray-Schauder fixed point theorem. ER -