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Steady flows of an Oldroyd fluid with threshold slip

This work was supported by the Russian Foundation for Basic Research, project no. 16-31- 00182 mol_a

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  • We consider a mathematical model that describes 3D steady flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain under mixed boundary conditions, including a threshold-slip boundary condition. Using the concept of weak solutions, we reduce the original slip problem to a coupled system of variational inequalities and equations for the velocity field and stresses. For arbitrary large data (forcing and boundary data) and suitable material constants, we prove the existence of weak solutions and establish some of their properties.

    Mathematics Subject Classification: Primary: 35Q35, 76A05; Secondary: 35A01.


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