Abstract
We investigate the evolution of cusp-like singularities in the boundary of a vortex patch for two-dimensional Euler equations. According to numerical simulations, cusp singularities appear as limit structures for the evolution of smooth vortex patches when the time goes to infinity. We here present an adaptive scheme that we have used to study the stability of the cusp. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a singular point, which generalises the structure of a cusp. This entails the global stability of the cusp with conservation of the order.
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© 1999 Springer Basel AG
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Danchin, R. (1999). Evolution of a Cusp-like Singularity in a Vortex Patch. In: Fey, M., Jeltsch, R. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 129. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8720-5_21
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DOI: https://doi.org/10.1007/978-3-0348-8720-5_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9742-6
Online ISBN: 978-3-0348-8720-5
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