### 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 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Houston Journal of Mathematics*,

*26*(2), 387-408.

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*Houston Journal of Mathematics*, vol. 26, no. 2, pp. 387-408.

**Existence of weak solutions to a class of non-Newtonian flows.** / Bae, Hyeong Ohk; Choe, Hi Jun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Existence of weak solutions to a class of non-Newtonian flows

AU - Bae, Hyeong Ohk

AU - Choe, Hi Jun

PY - 2000/12/1

Y1 - 2000/12/1

N2 - We show that there exist weak solutions to a class of non-Newtonian flows for the periodic domain. Galerkin approximation, an W1,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.

AB - We show that there exist weak solutions to a class of non-Newtonian flows for the periodic domain. Galerkin approximation, an W1,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.

UR - http://www.scopus.com/inward/record.url?scp=0040182712&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040182712&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 387

EP - 408

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 2

ER -