H\"older continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions

TL;DR

This paper proves the existence of solutions with H"older continuous velocity gradients and pressure for non-stationary shear-thinning fluid flows under perfect slip boundary conditions in a 2D domain, assuming specific stress tensor growth conditions.

Contribution

It establishes the H"older continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions, extending previous regularity results.

Findings

Existence of solutions with H"older continuous velocity gradients

Valid for stress tensor growth p in [5/3, 2]

Applicable to non-stationary shear-thinning flows

Abstract

This paper is concerned with non-stationary flows of sheart-hinning fluids in a bounded two-dimensional C^{2;1} domain. Assuming perfect slip boundary conditions, we provide a proof of the existence of a solution with the H\"older continuous velocity gradients and pressure under condition that a stress tensor satisfies power-law with growth p\in[5/3; 2].