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arXiv · 2104.05545

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

Thomas Eiter·Katharina Hopf·Alexander Mielke
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Abstract

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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Thomas Eiter, Katharina Hopf, Alexander Mielke. 2021-04-12. Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation. https://doi.org/10.1016/j.nonrwa.2021.103491

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