### Abstract

We show that there exist weak solutions to a class of non-Newtonian flows for the periodic domain. Galerkin approximation, an W^{1,r}+^{2} compactness theorem, and Korn type inequalities are main ingredients for the proof of the existence of weak solutions. Moreover, we estimate the Hausdorff dimension of the set of singular times for the weak solutions.

Original language | English |
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Pages (from-to) | 387-408 |

Number of pages | 22 |

Journal | Houston Journal of Mathematics |

Volume | 26 |

Issue number | 2 |

Publication status | Published - 2000 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Bae, H. O., & Choe, H. J. (2000). Existence of weak solutions to a class of non-Newtonian flows.

*Houston Journal of Mathematics*,*26*(2), 387-408.