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- W2007665767 abstract "In this paper, we will study the following geometric flow, obtained by Goldstein and Petrich while considering the evolution of a vortex patch in the plane under Euler's equations: $mathbf{X}_t=-k_smathbf{n}-frac{1}{2}k^2mathbf{T}$, with s being the arc-length parameter and k the curvature. Perelman and Vega proved in [J. Differential Equations, 235 (2007), pp. 56–73] that this flow has a one-parameter family of regular solutions that develop a corner-shaped singularity at finite time. We will give a method for reproducing numerically the evolution of those solutions, as well as the formation of the corner, showing several properties associated to them." @default.
- W2007665767 created "2016-06-24" @default.
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- W2007665767 date "2009-01-01" @default.
- W2007665767 modified "2023-09-27" @default.
- W2007665767 title "Numerical Study of a Flow of Regular Planar Curves That Develop Singularities at Finite Time" @default.
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- W2007665767 doi "https://doi.org/10.1137/080718693" @default.
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