Liouville-Type Results for a Two-Dimensional Stretching Eyring–Powell Fluid Flowing along the z-Axis.

Abstract

The purpose of this study is to establish Liouville-type results for a three-dimensional incompressible, unsteady flow described by the Eyring–Powell fluid equations. The fluid is studied in a plane Ωp while it moves along the z-axis. Therefore the main functions to analyze are given by u(x,y,z,t) and v(x,y,z,t) , belonging to Ωp . The results are obtained for globally bounded initial data as well as their corresponding derivatives, and the variations in velocity along the z-axis belong to the space L2 and BMO . Under such conditions, Liouville-type results are obtained and extended to Lp, p>2.