English

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}
}