Time-periodic weak solutions to incompressible generalized Newtonian fluids

TL;DR

This paper establishes the existence of time-periodic weak solutions for three-dimensional generalized Newtonian fluids with power-law viscosity, under periodic forcing, for viscosity exponents greater than 6/5.

Contribution

It develops an existence theory for periodic weak solutions to 3D generalized Newtonian fluids with power-law viscosity, extending the range of known exponents for such solutions.

Findings

Existence of periodic weak solutions for q>6/5

Optimal bound for weak solution existence

Applicable to three-dimensional generalized Newtonian fluids

Abstract

In this study we are interested in the Navier-Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of periodic in time weak solutions to the three-dimensional flows subject to a periodic in time force datum whenever q>6/5, which is the optimal bound for the existence of weak solutions.