Jeffreys fluids in forced elongation

In this paper we study existence, uniqueness and regularity of solutions for the equations governing the forced elongation of fluids with differential constitutive law of Jeffreys type. These equations consist of nonlinear first-order hyperbolic equations in one spatial dimension. Forced elongation...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2003-12, Vol.288 (2), p.634-645
Main Author: Hagen, Thomas
Format: Article
Language:English
Subjects:
Energy estimates
Exact sciences and technology
Existence theory
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematics
Non-newtonian fluid flows
Partial differential equations
Physics
Schauder fixed point theorem
Sciences and techniques of general use
Viscoelasticity
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Summary:In this paper we study existence, uniqueness and regularity of solutions for the equations governing the forced elongation of fluids with differential constitutive law of Jeffreys type. These equations consist of nonlinear first-order hyperbolic equations in one spatial dimension. Forced elongation is imposed through velocity boundary conditions at the domain entry and exit. The existence result is based on the Schauder fixed point theorem and energy methods in the space of boundary-regular functions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2003.09.018