Logarithmic estimates for continuity equations
Abstract
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coefficient. Second, we show how the ideas in [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] can be used to provide an alternative proof of the result in [Clop, Jiang, Mateu, and Orobitg, Calc. Var. Partial Differential Equations 2016], [Desjardins, Comm. Partial Diff. Eq. 1996], and [Mucha, J. Differential Equations 2010] where the usual requirement of boundedness of the divergence of the vector field has been relaxed to various settings of exponentially integrable functions.
Cite
@article{arxiv.1811.02463,
title = {Logarithmic estimates for continuity equations},
author = {Maria Colombo and Gianluca Crippa and Stefano Spirito},
journal= {arXiv preprint arXiv:1811.02463},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1411.0451