Partial regularity of weak solutions of the viscoelastic Navier-Stokes equations with damping

TL;DR

This paper extends partial regularity results to weak solutions of a viscoelastic fluid model with damping, aiding the understanding of global solution existence for complex fluid systems.

Contribution

It establishes a Caffarelli-Kohn-Nirenberg type theorem for a viscoelastic Navier-Stokes system with damping, advancing partial regularity theory for such PDEs.

Findings

Proved partial regularity for weak solutions

Extended classical regularity results to viscoelastic systems with damping

Provided a framework for analyzing global existence of solutions

Abstract

We prove an analog of the Caffarelli-Kohn-Nirenberg theorem for weak solutions of a system of PDE that model a viscoelastic fluid in the presence of an energy damping mechanism. The system was recently introduced as a possible method of establishing the global in time existence of weak solutions of the well known Oldroyd system.