Leray-Hopf solutions to a viscoelastoplastic fluid model withnonsmooth stress-strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The stateis given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba-Jaumann derivative. Moreover, the stress tensor obeysa nonlinear and nonsmooth dissipation law as well as stress diffusion. We provethe existence of global-in-time weak solutions satisfying an energy inequality undergeneral Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.(c) 2021 Elsevier Ltd. All rights reserved.