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Equations for Viscoelastic Fluids

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Abstract

This chapter aims at the mathematical theory of incompressible viscoelastic fluids and related complex fluid models. An energetic variational approach is employed to derive the hydrodynamics of complex fluids which focuses on the competition and coupling between different physical effects. Such a framework also provides guides to the corresponding analysis. This chapter includes those analytical results for both classical solutions with small initial data and weak solutions with large initial data for these systems.

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Acknowledgements

The work of Xianpeng Hu is partially supported by the start-up grant from City University of Hong Kong and the ECS grant 9048035. The work of Fanghua Lin is partially supported by the NSF grants DMS-1501000. The work of Chun Liu is partially supported by NSF grants DMS-141200 and DMS-1216938.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Office: P6715 Academic 1, Tat Chee Avenue, Hong Kong, China

    Xianpeng Hu

  2. Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY, USA

    Fang-Hua Lin

  3. Department of Mathematics, Pennsylvania State University, University Park, PA, USA

    Chun Liu

  4. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, USA

    Chun Liu

Authors
  1. Xianpeng Hu
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  2. Fang-Hua Lin
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  3. Chun Liu
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Correspondence to Xianpeng Hu .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan

    Yoshikazu Giga

  2. Université de Toulon IMATH, Toulon, France

    Antonín Novotný

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Hu, X., Lin, FH., Liu, C. (2018). Equations for Viscoelastic Fluids. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_25

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