@inproceedings{1e731924ac5346ceaa291d3574a210e3,

title = "Quantitative estimates for advective equation with degenerate anelastic constraint",

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{\textquoteright} 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.",

author = "Didier Bresch and Jab{\'i}n, {Pierre Emmanuel}",

note = "Funding Information: D. Bඋൾඌർඁ is partially supported by the ANR-16-CE06-0011 project FRAISE and P.–E. Jൺൻංඇ is partially supported by NSF Grants 1312142 and 161453 and by NSF Grant RNMS (Ki-Net) 1107444. MSC2010: primary 35B40; secondary 35B45, 35K35, 76Y05. Keywords: Quantitative regularity estimates, advective equation, degenerate anelastic constraint, vacuum state, stability property, lake equations, vanishing topography, renormalized solutions. Publisher Copyright: {\textcopyright} Proceedings of the International Congress of Mathematicians, ICM 2018. All rights reserved.; 2018 International Congress of Mathematicians, ICM 2018 ; Conference date: 01-08-2018 Through 09-08-2018",

year = "2018",

language = "English (US)",

series = "Proceedings of the International Congress of Mathematicians, ICM 2018",

publisher = "World Scientific Publishing Co. Pte Ltd",

pages = "2185--2213",

editor = "Boyan Sirakov and {de Souza}, {Paulo Ney} and Marcelo Viana",

booktitle = "Invited Lectures",

address = "Singapore",

}