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Optimal stability estimates for continuity equations

  • Christian Seis (a1)

Abstract

This review paper is concerned with the stability analysis of the continuity equation in the DiPerna–Lions setting in which the advecting velocity field is Sobolev regular. Quantitative estimates for the equation were derived only recently, but optimality was not discussed. We revisit the results from our 2017 paper, compare the new estimates with previously known estimates for Lagrangian flows and demonstrate how these can be applied to produce optimal bounds in applications from physics, engineering and numerical analysis.

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Present address: Institut für Analysis und Numerik, Universität Münster, Orléans-Ring 10, 48149 Münster, Germany (seis@wwu.de).

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* Present address: Institut für Analysis und Numerik, Universität Münster, Orléans-Ring 10, 48149 Münster, Germany ().

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