### Abstract

For any ɛ > 0 we show the existence of continuous periodic weak solutions v of the Euler equations that do not conserve the kinetic energy and belong to the space (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-Hölder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).

Original language | English (US) |
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Pages (from-to) | 1613-1670 |

Number of pages | 58 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 69 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2016 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Buckmaster, T., De Lellis, C., & Székelyhidi, L. (2016). Dissipative Euler Flows with Onsager-Critical Spatial Regularity.

*Communications on Pure and Applied Mathematics*,*69*(9), 1613-1670. https://doi.org/10.1002/cpa.21586