Global Well-Posedness for 2-D Viscoelastic Fluid Model

TL;DR

This paper establishes the global existence and uniqueness of weak solutions for a 2-D viscoelastic fluid model, providing a rigorous mathematical foundation for understanding such flows.

Contribution

It proves the first comprehensive global well-posedness result for the Oldroyd-type viscoelastic fluid model in two dimensions.

Findings

Existence of global weak solutions

Uniqueness of solutions

Derivation of the energy equation

Abstract

This paper is concerned with a mathematical model which describes 2-D flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain. We prove the existence and uniqueness theorem for global (in time) weak solutions and derive the energy equation.