Well‐posedness of the upper convected Maxwell fluid in the limit of infinite Weissenberg number |
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Authors: | Xiaojun Wang Michael Renardy |
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Institution: | Department of Mathematics, Virginia Tech, Blacksburg, VA 24061‐0123, U.S.A. |
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Abstract: | 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=qqT, q∈?n, and develop energy estimates to show that the problem is locally well‐posed. This problem is related to incompressible ideal magnetohydrodynamics (MHD). We show that the general case T=CCT, C∈?n×n can be handled by a generalization of the method we developed. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | viscoelastic flow infinite Weissenberg number hypoelasticity characteristic boundary |
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