Nonexistence of Self-Similar Singularities in the Ideal Viscoelastic Flow

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).