Title | Ill-posedness of Leray solutions for the ipodissipative Navier–Stokes equations |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | Colombo M., De Lellis C., De Rosa L. |

Journal | Communications in Mathematical Physics |

Volume | 362 |

Issue | 2 |

Pagination | 659–688 |

Date Published | September |

Publisher | Springer |

Type of Article | NS |

ISSN | 0010-3616 |

Keywords | Mathematical Physics, Statistical and Nonlinear Physics |

Abstract | We prove the ill-posedness of Leray solutions to the Cauchy problem for the hypodissipative Navier?Stokes equations and when the dissipative term is a fractional Laplacian \$(?\ensuremathΔ)\^ \ensuremathα\$ with exponent \$\ensuremathα\ensuremath<$\backslash$frac{1}{5}\$. The proof follows the ?convex integration methods? introduced by the second author and László Székelyhidi Jr. for the incompressible Euler equations. The methods yield indeed some conclusions even for exponents in the range \$[$\backslash$frac{1}{5}, $\backslash$frac{1}{2}[\$. |

Notes | Comm. Math. Phys. 362 (2018) no. 2, 659-688 |

URL | https://link.springer.com/article/10.1007/s00220-018-3177-x |

DOI | 10.1007/s00220-018-3177-x |

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