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Transactions of the American Mathematical Society

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Nonlinear stability of vortex patches

Author: Yun Tang
Journal: Trans. Amer. Math. Soc. 304 (1987), 617-638
MSC: Primary 76C05; Secondary 35B35, 35Q10
MathSciNet review: 911087
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Abstract: To establish the nonlinear (Liapunov) stability of both circular and elliptical vortex patches in the plane for the nonlinear dynamical system generated by the two-dimensional Euler equations of incompressible, inviscid hydrodynamics. This is accomplished by using a relative variational principle in terms of energy function. A counterexample shows that our result in the case of an elliptical vortex patch is the best one that can be attained by applying the energy estimate.

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Article copyright: © Copyright 1987 American Mathematical Society