Steady flows of an Oldroyd fluid with threshold slip

Evgenii S. Baranovskii

doi:10.3934/cpaa.2019036

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2019, Volume 18, Issue 2: 735-750. Doi: 10.3934/cpaa.2019036

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Steady flows of an Oldroyd fluid with threshold slip

Evgenii S. Baranovskii

Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, Voronezh, 394018, Russia

Received: February 2018

Revised: May 2018

Published: October 2018

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

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Abstract

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.

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

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