Behavior Near Time Infinity of Solutions of the Vorticity Equations

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 79)


The Navier–Stokes equations are famous as fundamental equations of fluid mechanics and have been well studied as typical nonlinear partial differential equations in mathematics. It is not too much to say that various mathematical methods for analyzing nonlinear partial differential equations have been developed through studies of the Navier–Stokes equations. There have been many studies of the behavior of solutions of the Navier–Stokes equations near time infinity. In this chapter, as an application of the previous section, we study the behavior of the vorticity of a two dimensional flow near time infinity. In particular, we study whether or not the vorticity converges to a self-similar solution.


Weak Solution Stokes Equation Heat Equation Asymptotic Formula Sobolev Inequality 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoMeguro-kuJapan
  2. 2.Technische Universität Darmstadt Center of Smart InterfacesDarmstadtGermany

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