A quantitative theory for the continuity equation
Analysis of PDEs
2017-01-30 v3
Abstract
In this work, we provide stability estimates for the continuity equation with Sobolev vector fields. The results are inferred from contraction estimates for certain logarithmic Kantorovich--Rubinstein distances. As a by-product, we obtain a new proof of uniqueness in the DiPerna--Lions setting. The novelty in the proof lies in the fact that it is not based on the theory of renormalized solutions.
Cite
@article{arxiv.1602.02931,
title = {A quantitative theory for the continuity equation},
author = {Christian Seis},
journal= {arXiv preprint arXiv:1602.02931},
year = {2017}
}
Comments
Final version, includes optimality result. Accepted for publication in Annales IHP