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In this article, we introduce the concept of energy-variational solutions fora large class of systems of nonlinear evolutionary partial differentialequations. Under certain convexity assumptions, the existence of such solutionscan be shown constructively by an adapted minimizing movement scheme.Weak-strong uniqueness follows by a suitable relative energy inequality. Ourmain motivation is to apply the general framework to viscoelastic fluid models.Therefore, we give a short overview on different versions of such models andtheir derivation. The abstract result is applied to two of these viscoelasticfluid models in full detail. In the conclusion, we comment on furtherapplications of the general theory and its possible impact.

Energy-variational solutions for viscoelastic fluid models