A note on Liouville theorem for stationary flows of shear thickening fluids in the plane

TL;DR

This paper proves a Liouville theorem for stationary shear thickening fluid flows in the plane, showing that bounded solutions must be trivial, thereby extending understanding of such fluid dynamics.

Contribution

It establishes a Liouville theorem for entire weak solutions of shear thickening fluid equations under bounded velocity conditions, a novel result in this context.

Findings

Liouville theorem holds for bounded solutions

Weak solutions are trivial under boundedness

Extends understanding of shear thickening fluid flows

Abstract

In this paper we consider the entire weak solutions of the equations for stationary flows of shear thickening fluids in the plane and prove Liouville theorem under the global boundedness condition of velocity fields.