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The stability of rotating vortex patches. (English) Zbl 0624.76055
The paper mainly deals with nonlinear stability of rotating vortex patches. The stability is studied by using variational methods and spectral analysis. Several theorems are established, which generalize previous results obtained by Arnold. The cases of: (i) Kirchhoff vortex; (ii) finite Kelvin waves, are specially examined as applications. Many references are given, which relate this work to pevious works by Arnold, Benjamin and others.
Reviewer: P.A.Bois

76E30 Nonlinear effects in hydrodynamic stability
76B47 Vortex flows for incompressible inviscid fluids
35P99 Spectral theory and eigenvalue problems for partial differential equations
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