Title | Smoothing does not give a selection principle for transport equations with bounded autonomous fields |

Publication Type | Journal Article |

Year of Publication | 2022 |

Authors | De Lellis C, Giri V |

Journal | Ann. Math. Que'. |

Volume | 46 |

Type of Article | transport equations |

Abstract | We give an example of a bounded divergence free autonomous vector field in $\mathbb R^3$ (and of a nonautonomous bounded divergence free vector field in $\mathbb R^2$) and of a bounded initial data for which the Cauchy problem for the corresponding transport equation has 2 distinct solutions. We then show that both solutions are limits of classical solutions of transport equations for appropriate smoothings of the vector fields and of the initial data. |

Notes | Ann. Math. Que'. 46 (2022), no. 1, 27-39 A volume in honor of Alexander Shnirelman |

URL | https://link.springer.com/article/10.1007/s40316-021-00160-y |

DOI | 10.1007/s40316-021-00160-y |

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