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

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.

arXiv commentAccepted for publication in Nonlinear Anal. Real World Appl

References in corpus (4)

• Thermodynamics of viscoelastic rate-type fluids with stress diffusion
• On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion
• Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
• Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions

Cited by in corpus (4)

• Quasistatic hypoplasticity at large strains Eulerian
• Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models
• Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics
• The Stefan problem in a thermomechanical context with fracture and fluid flow