Quantitative estimates for advective equation with degenerate anelastic constraint

Didier Bresch, Pierre Emmanuel Jabín

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In these proceedings we are interested in quantitative estimates for advective equations with an anelastic constraint in presence of vacuum. More precisely, we derive a quantitative stability estimate and obtain the existence of renormalized solutions. Our main objective is to show the flexibility of the method introduced recently by the authors for the compressible Navier-Stokes’ system. This method seems to be well adapted in general to provide regularity estimates on the density of compressible transport equations with possible vacuum state and low regularity of the transport velocity field; the advective equation with degenerate anelastic constraint considered here is another good example of that. As a final application we obtain the existence of global renormalized solution to the so-called lake equation with possibly vanishing topography.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Pages2185-2213
Number of pages29
ISBN (Electronic)9789813272927
StatePublished - 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018
Volume3

Conference

Conference2018 International Congress of Mathematicians, ICM 2018
CountryBrazil
CityRio de Janeiro
Period8/1/188/9/18

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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