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Well-posedness of the upper convected Maxwell fluid in the limit of infinite Weissenberg number

✍ Scribed by Xiaojun Wang; Michael Renardy

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
222 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by W. Sprâßig

An iteration scheme is used to show the well-posedness of the initial-boundary value problem for incompressible hypoelastic materials, which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume that the stress is a rank-one matrix T = qq T ,q∈ R n , and develop energy estimates to show that the problem is locally wellposed. This problem is related to incompressible ideal magnetohydrodynamics (MHD). We show that the general case T = CC T ,C ∈ R nΓ—n can be handled by a generalization of the method we developed.

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