Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 93, pp. 1-7.

Title: Nonexistence of self-similar singularities in  ideal viscoelastic flows

Author: Anthony Suen (Indiana Univ., Bloomington, IN, USA)

Abstract:
 We prove the nonexistence of finite time self-similar singularities in
 an ideal viscoelastic flow in R^3.
 We exclude the occurrence of Leray-type self-similar singularities under
 suitable integrability conditions on velocity and deformation tensor.
 We also prove the nonexistence of asymptotically self-similar singularities
 in our system. The present work extends the results obtained by Chae in
 the case of magnetohydrodynamics (MHD).

Submitted November 16, 2011. Published June 07, 2012.
Math Subject Classifications: 35A20.
Key Words: Viscoelastic flow; self-similar singularities.