WIAS Preprint No. 2829, (2021)

Leray--Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation


  • Eiter, Thomas
    ORCID: 0000-0002-7807-1349
  • Hopf, Katharina
    ORCID: 0000-0002-6527-2256
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2020 Mathematics Subject Classification

  • 35K61 35Q35 76A10 76D03


  • Viscoelastic fluid, stress diffusion, viscoplasticity, inhomogeneous time-dependent boundary values, existence, weak solutions, energy inequality




We consider a fluid model including viscoelastic and viscoplastic effects. The state is 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 obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.

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