Regularity Criterion for a Two Dimensional Carreau Fluid Flow

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 viscoeslastic materials. The purpose this study is develop the global regularity criteria for fluid in two dimensions flowing strip. Firstly, shown initial set $$\left( u_{10},u_{20}\right) \in H^{1}\left( \Omega \right) $$ u 10 , 20 ∈ H 1 Ω where $$\Omega =\left[ 0,L\right] \times = 0 L × $$\left[ 0,\infty .$$ ∞ . Secondly, analysis focuses on when L^{4}\left( 4 and, lastly, similar results obtained H^{2}\left( 2 while velocity vertical component, $$u_2 (x,y)$$ ( x y ) , that $$\frac{\partial u_{2}}{\partial x}\in ∂ \frac{\partial \nabla y},\Delta u_{2}\right) L^{2}\left( ∇ Δ .