On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation
Analysis of PDEs
2024-05-28 v1
Abstract
This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical, critical and supercritical ranges. We study those three cases and obtain a set of results containing local well-posedness, global smoothness, eventual regularity and finite-time blowup of smooth solutions.
Keywords
Cite
@article{arxiv.2405.16364,
title = {On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation},
author = {Wanwan Zhang},
journal= {arXiv preprint arXiv:2405.16364},
year = {2024}
}