Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models

Abstract We study a model for fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of velocity symmetric deviatoric stress tensor. This tensor is transported via Zaremba-Jaumann rate, it subject to two dissipation processes: one induced by nonsmooth convex potential diffusion. show short-time existence strong solutions as well their uniqueness class Leray-Hopf-type weak satisfying tensorial component sense an evolutionary variational inequality. The global-in-time such generalized has been established previous work. further limit when diffusion vanishes. In this case, above notion no longer suitable, we introduce concept energy-variational solutions, based on inequality relative energy. derive general properties passing nondiffusive energy satisfied nonzero