@article{88d9b65c2501434dada7e341ec1125c6,
title = "Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum",
abstract = "We study the evolution of a compressible fluid surrounded by vacuum and introduce a new symmetrization in Lagrangian coordinates that allows us to encompass both relativistic and non-relativistic fluid flows. The problem under consideration is a free boundary problem of central interest in compressible fluid dynamics and, from the mathematical standpoint, the main challenge to be overcome lies in the loss of regularity in the fluid variables near the free boundary. Based on our Lagrangian formulation, we establish the necessary a priori estimates in weighted Sobolev spaces which are adapted to this loss of regularity.",
keywords = "Free boundary, Lagrangian formulation, Relativistic fluid, Vacuum state, Weighted energy",
author = "Juhi Jang and LeFloch, {Philippe G.} and Nader Masmoudi",
note = "Funding Information: The first author (JJ) was supported in part by NSF grants DMS-1212142 and DMS-1351898 and a von Neumann fellowship of the Institute for Advanced Study through the NSF grant DMS-1128155 . This work was done when the second author (PLF) enjoyed the hospitality of the Courant Institute of Mathematical Sciences, New York University. PLF also acknowledges financial support from the ANR grant SIMI-1-003-01 and the European Commission grant ITN-642768 . The third author (NM) was partially supported by the NSF grant DMS-1211806 . This material is based in part upon work supported by the National Science Foundation under the above awards. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",
year = "2016",
month = mar,
day = "15",
doi = "10.1016/j.jde.2015.12.004",
language = "English (US)",
volume = "260",
pages = "5481--5509",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "6",
}