On Optimal Estimates for the Laplace-Leray Commutator in Planar Domains with Corners
Abstract
For smooth domains, Liu et al. (Comm. Pure Appl. Math. 60: 1443-1487, 2007) used optimal estimates for the commutator of the Laplacian and the Leray projection operator to establish well-posedness of an extended Navier-Stokes dynamics. In their work, the pressure is not determined by incompressibility, but rather by a certain formula involving the Laplace-Leray commutator. A key estimate of Liu et al. controls the commutator strictly by the Laplacian in energy norm at leading order. In this paper we show that this strict control fails in a large family of bounded planar domains with corners. However, when the domain is an infinite cone, we find that strict control may be recovered in certain power-law weighted norms.
Keywords
Cite
@article{arxiv.0912.3958,
title = {On Optimal Estimates for the Laplace-Leray Commutator in Planar Domains with Corners},
author = {Elaine Cozzi and Robert L. Pego},
journal= {arXiv preprint arXiv:0912.3958},
year = {2010}
}
Comments
Changed the Latex format