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

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.

It has been accepted for publication in SCIENCE CHINA Mathematics