×

Existence of slow steady flows of viscoelastic fluids with differential constitutive equations. (English) Zbl 0577.76014

In this paper, we prove the existence of slow steady flows of certain viscoelastic fluids by using an iterative method. The basic idea is very similar to existence proofs for initial value problems in hyperbolic partial differential equations. We first show that all iterates are bounded and small in a certain norm, and we then show that the iteration converges in a weaker norm.

MSC:

76A10 Viscoelastic fluids
76M99 Basic methods in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Crochet, Ann. Rev. Fluid Mech. 15 pp 241– (1983)
[2] Giesekus, Rheol. Acta 21 pp 366– (1982)
[3] Green, J. Chem. Phys. 14 pp 80– (1946)
[4] Perturbation Theory for Linear Operators, Springer, 1966.
[5] The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, 1969.
[6] Leonov, Rheol. Acta 15 pp 85– (1976)
[7] Lodge, Trans. Faraday Soc. 52 pp 120– (1956)
[8] Niggemann, Math. Meth. Appl. Sci. 3 pp 200– (1981)
[9] Oldroyd, Proc. Roy. Soc. London A245 pp 278– (1958) · Zbl 0080.38805
[10] and , The Nonlinear Field Theories of Mechanics, in: (ed.), Handbuch der Physik III/3, Springer, 1965.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.