Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics
Analysis of PDEs
2017-01-03 v2
Abstract
We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of continuity properties of the Bogovskii -operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for Non-Newtonian fluids governed by constitutive laws, which are not necessarily power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.
Keywords
Cite
@article{arxiv.1401.4885,
title = {Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics},
author = {Dominic Breit and Andrea Cianchi},
journal= {arXiv preprint arXiv:1401.4885},
year = {2017}
}