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

Publication Type | Journal Article |

Authors | De Lellis C, Giri V |

Journal | To appear in Annales Math'ematiques du Que'bec |

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 | To appear in Annales Mathe'matiques du Que'bec |

Order:

6