Electron. J. Diff. Equ., Vol. 2012 (2012), No. 93, pp. 1-7.

Nonexistence of self-similar singularities in ideal viscoelastic flows

Anthony Suen

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 7, 2012.
Math Subject Classifications: 35A20.
Key Words: Viscoelastic flow; self-similar singularities.

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Anthony Suen
Department of Mathematics
Indiana University
Bloomington, IN 47405, USA
email: cksuen@indiana.edu

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