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arXiv · 1602.02931

A quantitative theory for the continuity equation

Christian Seis
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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.

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Christian Seis. 2016-02-09. A quantitative theory for the continuity equation. https://doi.org/10.1016/j.anihpc.2017.01.001

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