Regularity Criterion for a Two Dimensional Carreau Fluid Flow.
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2022
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Journal of Nonlinear Mathematical Physics
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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).
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Keywords
Carreau fuid, Two Dimensional fuid, Unsteady fow, Regularity criterion