Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum

Juhi Jang, Philippe G. LeFloch, Nader Masmoudi

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)5481-5509
Number of pages29
JournalJournal of Differential Equations
Volume260
Issue number6
DOIs
StatePublished - Mar 15 2016

Fingerprint

Compressible Fluid
A Priori Estimates
Fluid Flow
Flow of fluids
Vacuum
Regularity
Lagrangian Coordinates
Sobolev spaces
Fluids
Symmetrization
Formulation
Weighted Sobolev Spaces
Free Boundary Problem
Fluid Dynamics
Fluid dynamics
Free Boundary
Fluid
Necessary

Keywords

  • Free boundary
  • Lagrangian formulation
  • Relativistic fluid
  • Vacuum state
  • Weighted energy

ASJC Scopus subject areas

  • Analysis

Cite this

Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum. / Jang, Juhi; LeFloch, Philippe G.; Masmoudi, Nader.

In: Journal of Differential Equations, Vol. 260, No. 6, 15.03.2016, p. 5481-5509.

Research output: Contribution to journalArticle

@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",
year = "2016",
month = "3",
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",

}

TY - JOUR

T1 - Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum

AU - Jang, Juhi

AU - LeFloch, Philippe G.

AU - Masmoudi, Nader

PY - 2016/3/15

Y1 - 2016/3/15

N2 - 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.

AB - 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.

KW - Free boundary

KW - Lagrangian formulation

KW - Relativistic fluid

KW - Vacuum state

KW - Weighted energy

UR - http://www.scopus.com/inward/record.url?scp=84957442743&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957442743&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2015.12.004

DO - 10.1016/j.jde.2015.12.004

M3 - Article

AN - SCOPUS:84957442743

VL - 260

SP - 5481

EP - 5509

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 6

ER -