Asymptotic properties of the plane shear thickening fluids with bounded energy integral
Abstract
In this note we investigate the asymptotic behavior of plane shear thickening fluids around a bounded obstacle. Different from the Navier-Stokes case considered by Gilbarg-Weinberger in GW1978, where the good structure of the vorticity can be exploited and weighted energy estimates can be applied, we have to overcome the nonlinear term of high order. The decay estimates of the velocity was obtained by combining Point-wise Behavior Theorem in Galdi and Brezis-Gallouet inequality in BG1980 together, which is independent of interest.
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