Nonlinear stability of vortex patches
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- by Yun Tang
- Trans. Amer. Math. Soc. 304 (1987), 617-638
- DOI: https://doi.org/10.1090/S0002-9947-1987-0911087-X
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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.References
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Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 304 (1987), 617-638
- MSC: Primary 76C05; Secondary 35B35, 35Q10
- DOI: https://doi.org/10.1090/S0002-9947-1987-0911087-X
- MathSciNet review: 911087