Research output: Research - peer-review › Article

In this article we present a new kind of regularity criterion for the global
well-posedness problem of the three-dimensional Navier--Stokes equations in
the whole space. It is shown that if for every fixed $t\in (0,T)$, the region
$\Omega:=\{(x,t)\mid |u(x,t)|>C(q)\norm{u}_{L^{3 q-6}}\}$, for some $C(q)$ appropriately defined, shrinks fast enough as $q\nearrow \infty$, then the
solution remains regular beyond $T$. The novelty of this new criterion is
that it involves the shape of the magnitude of the velocity. We argue that
reasonable flows satisfy our criterion, and singularity in Navier--Stokes
flows is highly unlikely.

Original language | English |
---|---|

Number of pages | 15 |

Journal | Nonlinearity |

State | Published - 2018 |

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