Abstract
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.
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© 2010 Springer Science+Business Media, LLC
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Giga, MH., Giga, Y., Saal, J. (2010). Behavior Near Time Infinity of Solutions of the Vorticity Equations. In: Nonlinear Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 79. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4651-6_2
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DOI: https://doi.org/10.1007/978-0-8176-4651-6_2
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4173-3
Online ISBN: 978-0-8176-4651-6
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