Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings

TL;DR

This paper investigates the regularity of weak solutions to generalized steady Stokes-type systems involving p-Laplacian, providing new regularity estimates in generalized Lorentz and Morrey spaces for incompressible Newtonian fluids.

Contribution

It offers new regularity results for nonlinear Stokes-type systems in advanced function spaces, covering both nonlinear and asymptotically regular cases.

Findings

Regularity estimates for velocity gradient and pressure in Lorentz spaces.

Results applicable to nonlinear and asymptotically regular problems.

Enhanced understanding of fluid flow regularity in generalized function settings.

Abstract

A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper also provides a relatively complete picture of our main results in two regards: problems with nonlinearity is regular with respect to the gradient variable; and asymtotically regular problems, whose nonlinearity satisfies a particular structure near infinity. For such Stokes-type systems, we derive regularity estimates for both velocity gradient and its associated pressure in two special classes of function spaces: the generalized Lorentz and $\psi$-generalized Morrey spaces.