Asymptotic behaviour of a Bingham fluid in thin layers

Abstract

A nonlinear stationary model describing the behaviour of a Bingham fluid is considered in a thin layer in R³. The limit problem obtained after transforming the original problem into one posed over a fixed reference domain and then letting ε (the parameter representing the thickness of the layer) tend to zero is studied. Existence and uniqueness results and a lower-dimensional 'Bingham-like' constitutive law are obtained. An identical study of a two-dimensional problem yields a one-dimensional model prevalent in engineering literature.