Energy-variational solutions for viscoelastic fluid models

Abstract

In this article, we introduce the concept of energy-variational solutions for a class of nonlinear dissipative evolutionary equations, which turns out to be especially suited to treat viscoelastic fluid models. Under certain convexity assumptions, the existence of such solutions can be shown constructively by an adapted minimizing movement scheme in a general framework. Weak-strong uniqueness follows by a suitable relative energy inequality. Our main motivation is to apply the general framework to viscoelastic fluid models. Therefore, we give a short overview on different versions of such models and their derivation. The abstract result is applied to two of these viscoelastic fluid models in full detail. In the conclusion, we comment on further applications of the general theory and its possible impact.