Liouville-Type Results for a Three-Dimensional Eyring-Powell Fluid with Globally Bounded Spatial Gradients in Initial Data

Abstract

The analysis in the present paper provides insights into the Liouville-type results for an Eyring-Powell fluid considered as having an incompressible and unsteady flow. The gradients in the spatial distributions of the initial data are assumed to be globally (in the sense of energy) bounded. Under this condition, solutions to the Eyring-Powell fluid equations are regular and bounded under the L2 norm. Additionally, a numerical assessment is provided to show the mentioned regularity of solutions in the travelling wave domain. This exercise serves as a validation of the analytical approach firstly introduced.

Keywords

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