## Abstract

We prove that given initial data (Formula presented.), forcing (Formula presented.) and any T > 0, the solutions u^{ν} of Navier-Stokes converge strongly in (Formula presented.) for any p ∈ [1, ∞) to the unique Yudovich weak solution u of the Euler equations. A consequence is that vorticity distribution functions converge to their inviscid counterparts. As a by-product of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the L^{p} vorticity topology. The main tool in these proofs is a uniformly controlled loss of regularity property of the linear transport by Yudovich solutions. Our results provide a partial foundation for the Miller-Robert statistical equilibrium theory of vortices as it applies to slightly viscous fluids.

Original language | English (US) |
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Pages (from-to) | 60-82 |

Number of pages | 23 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 75 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2022 |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- Applied Mathematics