A Nonlocal Friction Problem for a Class of Non-Newtonian Flows

L. Consiglieri

Abstract: In this work we study the flow for a class of non-Newtonian fluids with a nonlocal friction condition obtained by the mollification of the normal stresses on part of the boundary. Considering a reformulated problem using an abstract boundary operator, we prove an existence result for the steady case. The mathematical framework of the paper is mainly constituted by the duality theory of convex analysis and an application of a fixed point theorem to multivalued mappings.

Keywords: non-Newtonian fluids; nonlocal friction law and variational methods.

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