Regularity Criterion for a Two Dimensional Carreau Fluid Flow.

Abstract

Carreau fuids are a source of research from both theoretical and applied approaches. They have been considered to model diferent non-newtonian phenomena such as blood fow, plasma and viscoeslastic materials. The purpose of this study is to develop the global regularity criteria for a Carreau fuid in two dimensions fowing in a strip. Firstly, a regularity criteria is shown for the initial set ( u10, u20) ∈ H1(Ω) where Ω = [0, L]× [0, ∞). Secondly, the analysis focuses on a regularity criteria when ( u10, u20) ∈ L4(Ω) and, lastly, similar results are obtained for ( u10, u20) ∈ H2(Ω) while the fuid velocity vertical component, u2(x, y), is such that 휕u2 휕x ∈ L4(Ω) and (휕∇u2 휕y , Δu2 ) ∈ L2(Ω).