Free energies and asymptotic behaviour for incompressible viscoelastic fluids

Abstract

The existence, uniqueness and asymptotic stability for an incompressible, linear viscoelastic fluid is studied using a new free energy, the representation of which is based on the concept of a minimal state. A restriction imposed by thermodynamics is also used. Furthermore, an expression for the minimum free energy in the time domain is derived, which shows explicitly its dependence on the minimal state.

Keywords:

• viscoelastic fluid
• fading memory
• free energy
• behaviour of solutions

AMS Subject Classifications::

• 74D05
• 76A10
• 30E20
• 35B40

Acknowledgements

G. Amendola, M. Fabrizio and B. Lazzari were supported by I.N.d.A.M. and M.I.U.R. and J.M. Golden was supported by Dublin Institute of Technology for this study.

Notes

Note

1. It is possible to define the spaces and in the time domain by observing that where is defined by