Liouville theorems for stationary flows of shear thickening fluids in 2D

TL;DR

This paper proves Liouville theorems for stationary shear thickening fluid flows in 2D, showing that under certain energy and integrability conditions, solutions must be trivial.

Contribution

It establishes new Liouville theorems for 2D shear thickening fluids under energy and integrability constraints, extending understanding of such flows.

Findings

Weak solutions are trivial under finite energy conditions

Liouville theorems hold for solutions with specific integrability properties

Results contribute to the mathematical theory of non-Newtonian fluid flows

Abstract

In this paper we consider the entire weak solutions $u$ of the equations for stationary flows of shear thickening fluids in the plane and prove Liouville theorems under the conditions on the finiteness of energy and under the integrability condition of the solutions.