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 [18], 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 [16] and Brezis-Gallouet inequality in [7] together, which is independent of interest.