Abstract

Carreau fluids are a source of research from both theoretical and applied approaches. They have been considered to model different non-newtonian phenomena such as blood flow, plasma and viscoeslastic materials. The purpose of this study is to develop the global regularity criteria for a Carreau fluid in two dimensions flowing in a strip. Firstly, a regularity criteria is shown for the initial set left( u_{10},u_{20}right) in H^{1}left( Omega right) where Omega =left[ 0,Lright] times left[ 0,infty right) . Secondly, the analysis focuses on a regularity criteria when left( u_{10},u_{20}right) in L^{4}left( Omega right) and, lastly, similar results are obtained for left( u_{10},u_{20}right) in H^{2}left( Omega right) while the fluid velocity vertical component, u_2 (x,y), is such that frac{partial u_{2}}{partial x}in L^{4}left( Omega right) and left( frac{partial nabla u_{2}}{partial y},Delta u_{2}right) in L^{2}left( Omega right) .

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