Existence, regularity and uniqueness of weak solutions for a class of incompressible generalized Navier-Stokes system with slip boundary conditions in $\mathbb{R}^3_+$

TL;DR

This paper proves the existence, regularity, and uniqueness of weak solutions for a class of non-Newtonian power law fluids with slip boundary conditions in a half-space, advancing understanding of such fluid dynamics problems.

Contribution

It establishes the mathematical well-posedness of non-Newtonian fluid flow models with slip boundary conditions in three-dimensional half-space.

Findings

Existence of weak solutions proven for p > 9/5

Solutions exhibit regularity under specified conditions

Uniqueness of solutions demonstrated in the considered setting

Abstract

We obtain the existence, regularity, uniqueness of the non-stationary problems of a class of non-Newtonian fluid is a power law fluid with $p>9/5$ in the half-space under slip boundary conditions.