Uniqueness of signed measures solving the continuity equation for Osgood vector fields
Dynamical Systems
2009-02-11 v1 Analysis of PDEs
Abstract
Nonnegative measure-valued solutions of the continuity equation are uniquely determined by their initial condition, if the characteristic ODE associated to the velocity field has a unique solution. In this paper we give a partial extension of this result to signed measure-valued solutions, under a quantitative two-sided Osgood condition on the velocity field. Our results extend those obtained for log-Lipschitz vector fields by Bahouri and Chemin.
Cite
@article{arxiv.0807.1592,
title = {Uniqueness of signed measures solving the continuity equation for Osgood vector fields},
author = {Luigi Ambrosio and Patrick Bernard},
journal= {arXiv preprint arXiv:0807.1592},
year = {2009}
}