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The paper is devoted to the study of asymptotic behaviour of the solution of two dimensional steady flow of Herschel-Bulkley fluid through a thin layer. We prove some convergence results when the thicness tends to zero and we give the mechanical interpretation of the results.

Mathematics Subject Classification (2010): 76A05, 76A20, 35B40.

Keywords: asymptotic behaviour, Herschel-Bulkley fluid, thin layer.