Research output: Research - peer-review › Article

This study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(*t*) := {x : |*u*(*x*, *t*)| > *c* ||*u*||_{Lr(R}3_{)} }, for some *r* ≥ 3 and constant *c* independent of *t*, with measure |Ω|. It is shown that if ||*p* + *P*||_{L}3/2_{(Ω)} becomes sufficiently small as |Ω| decreases, then||*u*||_{L}(r+6)/3_{(R}3_{)} decays and regularity is secured. Here *p* is the physical pressure and *P* is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |*p* + *P*| within Ω are deduced.

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

Pages (from-to) | 21-27 |

Number of pages | 7 |

Journal | Applied Mathematics Letters |

Volume | 67 |

Early online date | 1 Dec 2016 |

DOIs | |

State | Published - May 2017 |

- Navier-Stokes equations, Hölder continuity , Global regularity

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