## Abstract

Recent numerical simulations have shown the existence of multiple self-similar solutions to the Cauchy problem for the 2-dimensional incompressible Euler equation, with initial vorticity in L_{loc}^{p}(R^{2}), 1≤p<+∞. Toward a rigorous validation of these computations, in this paper we analytically construct self-similar solutions (i) on an outer domain of the form {|x|>R}, and (ii) in a neighborhood of the points where the solution exhibits a spiraling vortex singularity. The outer solution is obtained as the fixed point of a contractive transformation, based on the Biot-Savart formula and integration along characteristics. The inner solution is constructed using a system of adapted coordinates, following the approach of V. Elling (2016) [17].

Original language | English (US) |
---|---|

Pages (from-to) | 5142-5203 |

Number of pages | 62 |

Journal | Journal of Differential Equations |

Volume | 269 |

Issue number | 6 |

DOIs | |

State | Published - Sep 5 2020 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics