Nonexistence of Self-Similar Singularities in the Ideal Viscoelastic Flow

TL;DR

This paper proves that ideal viscoelastic flow in three dimensions cannot develop finite-time self-similar singularities under certain conditions, extending previous results from magnetohydrodynamics.

Contribution

It establishes the nonexistence of self-similar singularities in ideal viscoelastic flow, generalizing prior work to this specific fluid model.

Findings

No finite-time self-similar singularities occur under certain integrability conditions.

Leray-type self-similar singularities are excluded in the model.

Asymptotically self-similar singularities are also shown not to exist.

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).