Description

• Tytuł:
  On global regular solutions to the Navier-Stokes equations in cylindrical domains
• Twórca:
  Zajączkowski, Wojciech M.
• Opis:
  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.
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Data:
  2011.04.23
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  English
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 37, No 1 (March 2011); 55 - 85;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.003/8393
• Temat i słowa kluczowe:
  Navier-Stokes equations;
  existence of regular solutions;
  global existence;
  slip boundary conditions;
  76D03;
  76D05;
  35Q30
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.003
• Dostawca danych:
  Akademicka Platforma Czasopism
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