Existence of weak solutions for non-stationary flows of fluids with shear thinning dependent viscosities under slip boundary conditions in half space

TL;DR

This paper proves the existence of weak solutions for non-Newtonian, shear-thinning fluids with slip boundary conditions in a half-space, using approximation and truncation methods for certain p-potential flows.

Contribution

It establishes the existence of weak solutions for non-Newtonian fluids with shear-thinning viscosities under slip boundary conditions, expanding mathematical understanding of such flows.

Findings

Existence of weak solutions for p in (8/5, 2]

Applicable to large initial data

Uses Oseen-type approximation and $L^ Infty$-truncation method

Abstract

The author treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by $p-$potential function subject to slip boundary conditions in $\mathbb{R}^3_+$. Making use of the Oseen-type approximation to this model and the $L^\infty$-truncation method, one can establish the existence theorem of weak solutions for $p-$potential flow with $p\in(\frac{8}{5},2]$ provided that large initial data.