On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph. (English) Zbl 1296.35137

Robinson, James C. (ed.) et al., Mathematical aspects of fluid mechanics. Selected papers based on the presentations at the workshop partial differential equations and fluid mechanics, Warwick, UK, June 15–19, 2010. Cambridge: Cambridge University Press (ISBN 978-1-107-60925-9/pbk). London Mathematical Society Lecture Note Series 402, 23-51 (2012).
Summary: We study flows of incompressible fluids in which the deviatoric part of the Cauchy stress and the symmetric part of the velocity gradient are related through an implicit equation. Although we restrict ourselves to responses characterized by a maximal monotone graph, the structure is rich enough to include power-law type fluids, stress power-law fluids, Bingham and Herschel-Bulkley fluids, etc. We are interested in the development of (large-data) existence theory for internal flows subject to no-slip boundary conditions. We study first Stokes-like problems wherein the inertial effects are neglected, and later we consider the full balance of linear momentum that includes the inertial term.
For the entire collection see [Zbl 1254.76008].


35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids