Leray--Hopf solutions to a viscoelastic fluid model with nonsmooth stress-strain relation
- Eiter, Thomas
- Hopf, Katharina
- Mielke, Alexander
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.
- Nonlinear Anal. Real World Appl., 65 (2022), pp. 103491/1--103491/30 (published online on 20.12.2021), DOI 10.1016/j.nonrwa.2021.103491 .