Liouville-Type Results for a Two-Dimensional Stretching Eyring–Powell Fluid Flowing along the <i>z</i>-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.

Keywords

• Liouville-type results
• Eyring–Powell fluid
• three-dimensional flow
• unsteady flow