Existence of steady solutions of Newtonian and Non-Newtonian fluids with right hand sides beyond duality

Claudiu Mindrila, Sebastian Schwarzacher

Published 2019-11-05Version 1

We provide new a-priori estimates for classical Navier-Stokes equations as well as non-Newtonian fluids of power law type with right-hand sides that are not in the natural existence class. The estimates for the Navier-Stokes equation follows by a newly developed comparison method. For the estimates we make use of a newly developed solenoidal Lipschitz truncation (more explicit a relative truncation) that preserves zero boundary values. The estimates imply respective existence results for very weak right hand sides.