Global solutions to the Navier–Stokes- ${\bar \omega}$ and related models wi

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• 作者：Jishan Fan (1)
  Fucai Li (2)
  Gen Nakamura (3)
  
• 关键词：35Q30 ; 76D03 ; Navier–Stokes ; $${\bar \omega}$$ model ; Navier–Stokes ; α ; like models ; Magnetohydrodynamic ; α model ; Rough initial data ; Global Well ; posedness
• 刊名：Zeitschrift f篓鹿r angewandte Mathematik und Physik
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：65
• 期：2
• 页码：301-314
• 全文大小：264 KB
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• 作者单位：Jishan Fan (1)
  Fucai Li (2)
  Gen Nakamura (3)
  
  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China
  2. Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China
  3. Department of Mathematics, Inha University, Incheon, 402-751, Korea
  
• ISSN：1420-9039

文摘

We establish the global well-posedness of the Navier–Stokes- ${\bar \omega}$ model with initial data ${u_0 \in H^{1-s}(\mathbb{R}^3)}$ with ${0 < s < \frac{1}{2}}$ which improves the existence results in Fan and Zhou (Appl Math Lett 24:1915-918, 2011), Layton et?al. (Commun Pure Appl Anal 10:1763-777, 2011) where the initial data are required belonging to ${H^2(\mathbb{R}^3)}$ . We also obtain the similar results for a family of Navier–Stokes-α-like and magnetohydrodynamic-α models.