Holm, Darryl D. and Marsden, Jerrold E. and Ratiu, Tudor (1986) Nonlinear stability of the Kelvin-Stuart cat's eyes flow. In: Nonlinear systems of partial differential equations in applied mathematics part 2. Lectures in Applied Mathematics. No.23. AMS , pp. 171-186. ISBN 0821811266 http://resolver.caltech.edu/CaltechAUTHORS:20100812-082932155
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Conditions which ensure the nonlinear stability of the Kelvin-Stuart cat's eyes solution for two dimensional ideal flow are given. The solution is periodic in the x direction and is bounded by two streamlines, which contain the separatrix, in the y-direction. The stability conditions are given explicitly in terms of the solution parameters and the domain size. The method is based on a technique originally developed by Arnold .
|Item Type:||Book Section|
|Additional Information:||© 1986 American Mathematical Society. Partially supported by DOE contract DE-AT03-32ER12097. Partially supported by and KSF postdoctoral fellowship. We thank John Gibbon for suggesting this problem and Jerry Kazdan for useful conversations about the Poincare inequality. We also thank George Nickel for making the figures.|
|Classification Code:||MSC: 76E30. 58F10|
|Official Citation:||Holm, Darryl D. ; Marsden, Jerrold E. ; Ratiu, Tudor S. In: Nonlinear systems of partial differential equations in applied mathematics, . Part 2, 1986, p. 171-186 Amer. Math. Soc., 1986. Series: Lectures in Appl. Math., vol. 23 Reference: CAG-CHAPTER-2008-001|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||13 Aug 2010 16:51|
|Last Modified:||26 Dec 2012 12:19|
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