Advances in Differential Equations

The minimum free energy for a class of compressible viscoelastic fluids

M. Fabrizio, G. Gentili, and J. M. Golden

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A general expression is derived for the isothermal minimum free energy of a compressible viscoelastic fluid with linear dependence on the history of strain and nonlinear dependence on the density. This involves the solution of a Wiener--Hopf integral equation, for which an existence and uniqueness theorem is proved. The factorization of a particular material tensor, which is fundamental to the methodology, can be carried out explicitly in this case.

Article information

Adv. Differential Equations Volume 7, Number 3 (2002), 319-342.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76A10: Viscoelastic fluids
Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D10: Boundary-layer theory, separation and reattachment, higher-order effects 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]


Fabrizio, M.; Gentili, G.; Golden, J. M. The minimum free energy for a class of compressible viscoelastic fluids. Adv. Differential Equations 7 (2002), no. 3, 319--342.

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