2012/02/06 by Wojciech M. Zajączkowski, Wojciech M. Zajaczkowski, Zajaczkowski, Wojciech M.
Computer Science · Engineering · Mathematics · #35Q30 #35Q35 #76D03 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35Q30 #msc:35Q35 #msc:76D03 #msc:76D05
paper · pdf · doi:10.48550/arxiv.1202.1085
37 pages
arxiv created 2012/02/06 · openalex publication_date 2012/02/06 · arxiv updated 2012/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the motion of incompressible viscous non-homogeneous fluid described by the Navier-Stokes equations in a bounded cylinder under boundary slip conditions. Assume that the third co-ordinate axis is the axis of the cylinder. Assuming that the derivatives of density, velocity, external force with respect to the third co-ordinate are sufficiently small in some norms we prove large time regular solutions without any restriction on the existence time. The proof is divided into two parts. First an a priori estimate is shown. Next the existence follows from the Leray-Schauder fixed point theorem.