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Mathematische Annalen

, Volume 357, Issue 2, pp 687–709 | Cite as

Global existence results for Oldroyd-B fluids in exterior domains: the case of non-small coupling parameters

  • Daoyuang Fang
  • Matthias HieberEmail author
  • Ruizhao Zi
Article

Abstract

Consider the set of equations describing Oldroyd-B fluids in an exterior domain. It is shown that this set of equations admits a unique, global solution in a certain function space provided the initial data, but not necessarily the coupling constant, is small enough.

Mathematics Subject Classification (2000)

35Q35 76D03 76D05 

Notes

Acknowledgments

This work was carried out while the first and the third authors are visiting the Department of Mathematics at the Technical University of Darmstadt. They would express their gratitude to Prof. Matthias Hieber for his kind hospitality and the Deutsche Forschungsgemeinschaft (DFG) for financial support. We would like thank Paolo Galdi for stimulating discussion concerning Oldroyd-B fluids and the third author also would like to thank Tobias Hansel for his sincere help. Daoyuan Fang and Ruizhao Zi were partially supported by NSFC 11271322, 10931007 and ZNSFC Z6100217.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Center of Smart InterfacesDarmstadtGermany

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