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.
Highlights
Numerous studies have been conducted on the Eyring-Powell fluid flow
There is not much literature focused on the development of the Liouville results for the velocity profiles of an Eyring-Powell fluid flowing along the z-axis
Such proposed theorem permitted us to state on the L2 -regularity criteria the given initial data with the energetically bounded spatial gradient
Summary
Fluids such as air, oil, and water are typically formulated following a Newtonian description. The particular description of a viscosity term leads to different fluid conceptions under the general definition of non-Newtonian fluids This is the case of the fluid studied in the presented analysis known as the Eyring-Powell flow. There is not much literature focused on the development of the Liouville results for the velocity profiles of an Eyring-Powell fluid flowing along the z-axis. There is extensive literature developing the regularity criteria and Liouville-type results for stationary fluids under Navier–Stokes Newtonian descriptions. In this regard, the reader can refer to the applications to Magnetohydrodynamics (MHD) and Hall-MHD in [11–16].
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