Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the velocity an internal stress tensor that transported along flow with Zaremba-Jaumann derivative. Moreover, obeys nonlinear nonsmooth dissipation law as well diffusion. prove existence of global-in-time weak solutions satisfying energy inequality under general Dirichlet conditions for field Neumann tensor.