### Abstract

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of satisfying the strong energy inequality. Extending previous results Farwig et al., Journal of Mathematical Fluid Mechanics, 2007, to appear we prove among other things that u is regular if either the kinetic energy or the dissipation energy is (left-side) HÖlder continuous as a function of time t with HÖlder exponent 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 |

Subtitle of host publication | Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday |

Publisher | Springer Berlin Heidelberg |

Pages | 215-227 |

Number of pages | 13 |

ISBN (Print) | 9783642040672 |

DOIs | |

Publication status | Published - 2010 Dec 1 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Farwig, R., Kozono, H., & Sohr, H. (2010). Regularity of weak solutions for the Navier-Stokes equations via energy criteria. In

*Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday*(pp. 215-227). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-04068-9_13