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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DOI:
https://doi.org/10.1090/S0002-9947-1987-0911087-X

Article copyright:
© Copyright 1987
American Mathematical Society