TY - JOUR
AU - Rencławowicz, Joanna
AU - Zajączkowski, Wojciech M.
PY - 2008/09/01
Y2 - 2023/03/25
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 -