### Abstract

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of R^{3} satisfying the strong energy inequality. Extending previous results by Farwig et al., J. Math. Fluid Mech. 11, 1-14 (2008), we prove among other things that u is regular if either the kinetic energy 1/2 ∥u(t) ∥^{2}
_{2} or the dissipation energy ∫ ^{t} _{0} ∥∇u(τ ) ∥^{2} _{2} dτ is (left-side) Hölder continuous as a function of time t with Hölder exponent 1/2 and with sufficiently small Hölder seminorm. The proofs use local regularity results which are based on the theory of very weak solutions and on uniqueness arguments for weak solutions.

Original language | English |
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Title of host publication | Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday |

Pages | 215-227 |

Number of pages | 13 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 2007 International Conference on Mathematical Fluid Mechanics - Estoril Duration: 2007 May 21 → 2007 May 25 |

### Other

Other | 2007 International Conference on Mathematical Fluid Mechanics |
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City | Estoril |

Period | 07/5/21 → 07/5/25 |

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### Keywords

- Energy criteria
- Hölder continuity
- Navier-Stokes equations
- Regularity criteria
- Weak solutions

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

*Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday*(pp. 215-227) https://doi.org/10.1007/978-3-642-04068-9-13