Existence Theory for Generalized Newtonian Fluids

Chapter 2

Fluid mechanics & Orlicz spaces

Abstract

We extend some classical tools from fluid mechanics – Korn's inequality, the Bogovskiĭ  operator and the pressure recovery – to the setting of Orlicz spaces. As a special case the known $L^p$-theory is included as well as the case of Orlicz spaces generated by a nice Young function (i.e., under ${\mathrm{\Delta }}_2$ and ${\mathrm{\nabla }}_2$ condition). In the general case there is some loss of integrability, for instance in the limit ...