Description

• Title:
  On global regular solutions to the Navier-Stokes equations in cylindrical domains
• Creator:
  Zajączkowski, Wojciech M.
• Description:
  We consider the incompressible fluid motion described by the Navier-Stokes equations in a cylindrical domain $\Omega\subset\R^3$ under the slip boundary conditions. First we prove long time existence of regular solutions such that $v\in W_2^{2,1}(\Omega\times(0,T))$, $\nabla p\in L_2(\Omega\times(0,T))$, where $v$ is the velocity of the fluid and $p$ the pressure. To show this we need smallness of $\|v_{,x_3}(0)\|_{L_2(\Omega)}$ and $\|f_{,x_3}\|_{L_2(\Omega\times(0,T))}$, where $f$ is the external force and $x_3$ is the axis along the cylinder. The above smallness restrictions mean that the considered solution remains close to the two-dimensional solution, which, as is well known, is regular. Having $T$ sufficiently large and imposing some decay estimates on $\|f(t)\|_{L_2(\Omega)}$ we continue the local solution step by step up to the global one.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2011.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 37, No 1 (March 2011); 55 - 85;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.003/8393
• Subject:
  Navier-Stokes equations;
  existence of regular solutions;
  global existence;
  slip boundary conditions;
  76D03;
  76D05;
  35Q30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.003
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other