Liouville-type theorems for steady flows of degenerate power law fluids in the plane

Abstract

We extend the Liouville-type theorems of Gilbarg and Weinberger and of Koch, Nadirashvili, Seregin and Sverák valid for the stationary variant of the classical Navier-Stokes equations in 2D to the degenerate power law fluid model.

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• Liouville theorem of axially symmetric Navier-Stokes equations with growing velocity at infinity
• Asymptotic properties of the plane shear thickening fluids with bounded energy integral