Free energies and asymptotic behaviour for incompressible viscoelastic fluids

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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: behaviour of solutions; fading memory; free energy; viscoelastic fluid

Document Type: Research Article


Affiliations: 1: Dipartimento di Matematica Applicata, 'U. Dini', University of Pisa, 56126-Pisa, Italy 2: Dipartimento di Matematica, University of Bologna, 40127-Bologna, Italy 3: Dublin Institute of Technology, Dublin 8, Ireland

Publication date: June 1, 2009

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