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Equations for Viscoelastic Fluids

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Xianpeng Hu

    (City University of Hong Kong, Department of Mathematics)

  • Fang-Hua Lin

    (New York University, Department of Mathematics, Courant Institute of Mathematical Sciences)

  • Chun Liu

    (Pennsylvania State University, Department of Mathematics
    Illinois Institute of Technology, Department of Applied Mathematics)

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.

Suggested Citation

  • Xianpeng Hu & Fang-Hua Lin & Chun Liu, 2018. "Equations for Viscoelastic Fluids," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 22, pages 1045-1073, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_25
    DOI: 10.1007/978-3-319-13344-7_25
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