On a 1D transport equation with nonlocal velocity and supercritical dissipation
Analysis of PDEs
2013-10-24 v3
Abstract
We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global regularity for solutions when dissipation is slightly supercritical. Both results utilize a nonlocal maximum principle.
Keywords
Cite
@article{arxiv.1304.4296,
title = {On a 1D transport equation with nonlocal velocity and supercritical dissipation},
author = {Tam Do},
journal= {arXiv preprint arXiv:1304.4296},
year = {2013}
}