Remarks on a nonlocal transport
Analysis of PDEs
2020-02-27 v1
Abstract
We consider a one dimensional nonlocal transport equation and its natural multi-dimensional analogues. By using a new pointwise inequality for the Hilbert transform, we give a short proof of a nonlinear inequality first proved by C\'{o}rdoba, C\'{o}rdoba and Fontelos in 2005. We also prove several new weighted inequalities for the Hilbert transform and various nonlinear versions. Some of these results generalize to a related family of nonlocal models.
Cite
@article{arxiv.2002.11305,
title = {Remarks on a nonlocal transport},
author = {Dong Li and Jose Rodrigo},
journal= {arXiv preprint arXiv:2002.11305},
year = {2020}
}
Comments
19pages