Advances in Differential Equations

Some theoretical results concerning diphasic viscoelastic flows of the Oldroyd kind

Laurent Chupin

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We present several existence and uniqueness results for the equations satisfied by the three-dimensional non-Newtonian mixture of the Oldroyd kind. We study the coupling of the constitutive law, the Navier-Stokes equations and the Cahn-Hilliard equation which stands for a model of a multiphase non-Newtonian fluid. We prove that a strong local solution exists, but also that a global solution exists if the data are small enough. This last result is established even if the fluids are strongly elastic.

Article information

Adv. Differential Equations, Volume 9, Number 9-10 (2004), 1039-1078.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76A10: Viscoelastic fluids
Secondary: 35Q35: PDEs in connection with fluid mechanics 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76T99: None of the above, but in this section


Chupin, Laurent. Some theoretical results concerning diphasic viscoelastic flows of the Oldroyd kind. Adv. Differential Equations 9 (2004), no. 9-10, 1039--1078.

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