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Well‐posedness of the upper convected Maxwell fluid in the limit of infinite Weissenberg number
Author(s) -
Wang Xiaojun,
Renardy Michael
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1335
Subject(s) - weissenberg number , mathematics , limit (mathematics) , magnetohydrodynamics , compressibility , mathematical analysis , convergence (economics) , boundary value problem , generalization , physics , geometry , flow (mathematics) , mechanics , plasma , quantum mechanics , economics , economic growth
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 well‐posed. This problem is related to incompressible ideal magnetohydrodynamics (MHD). We show that the general case T = CC T , C ∈ℝ n × n can be handled by a generalization of the method we developed. Copyright © 2010 John Wiley & Sons, Ltd.