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

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.