Regularity and profiles of solutions to a higher order Eyring–Powell fluid with Darcy–Forchheimer porosity term

Abstract

A flow of Eyring–Powell type constitutes a remarkable area of analysis to model non-Newtonian processes in fluids. The associated diffusion term comes from the general kinetic theory of liquids and permits to account for a wider diffusivity, which is applicable for qualitatively low to higher shear stresses. The goal of the present article is to introduce a generalization of an Eyring–Powell fluid by the introduction of a porous reaction term (of Darcy–Forchheimer type) and a perturbation with a higher order operator. In particular, we consider that our model is an extension of a classical Eyring–Powell fluid in the same manner as introduced for other equations (see the extended Fisher–Kolmogorov model). The obtained equation is novel and requires analysis about existence, regularity and uniqueness of solutions. Stationary solutions are explored under the definition of a Hamiltonian. In addition, profiles of solutions are obtained with an exponential scaling that ends in a Hamilton–Jacobi equation. Eventually, some numerical assessments are introduced to validate the hypothesis done, and to discuss about the accuracy of the analytical approach followed.