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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Jang, Juhi¹  LeFloch, Philippe G.^2,3  Masmoudi, Nader⁴ 

[1] Univ So Calif, Dept Math, Los Angeles, CA 90058 USA

[2] Univ Paris 06, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75252 Paris, France

[3] Univ Paris 06, CNRS, 4 Pl Jussieu, F-75252 Paris, France

[4] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10011 USA

关键词: Relativistic fluid;    Vacuum state;    Free boundary;    Lagrangian formulation;    Weighted energy;   

DOI  :  10.1016/j.jde.2015.12.004

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free