Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian formulation and a priori estimates for relativistic fluid
  flows with vacuum   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.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn