Abstract
In this paper we consider steady vortex solutions for the ideal incompressible Euler equation in a planar bounded domain. By solving a variational problem for the vorticity, we construct steady vortex patches with opposite rotation directions concentrated at a strict local minimum point of the Kirchhoff–Routh function with \(k=2\). Moreover, we show that such steady vortex patches are in fact local maximizers of the kinetic energy among isovortical patches, which correlates stability to uniqueness.
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Acknowledgements
Daomin Cao was supported by NNSF of China Grant (No. 11831009) and Chinese Academy of Sciences by Grant QYZDJ-SSW-SYS021. Guodong Wang was supported by NNSF of China Grant (No.11771469).
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Cao, D., Wang, G. Steady vortex patches with opposite rotation directions in a planar ideal fluid. Calc. Var. 58, 75 (2019). https://doi.org/10.1007/s00526-019-1503-6
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DOI: https://doi.org/10.1007/s00526-019-1503-6