Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Transonic Solutions of Planetary Atmospheres in Hydrodynamic
  Region $\mbox{--}$ Hydrodynamic Escape Problem due to Gravity and Heat   The hydrodynamic escape problem (HEP), which is characterized by a free
boundary value problem of Euler equation with gravity and heat, is crucial for
investigating the evolution of planetary atmospheres. In this paper, the global
existence of transonic solutions to the HEP is established using the
generalized Glimm method. The new version of Riemann and boundary-Riemann
solvers, are provided as building blocks of the generalized Glimm method by
inventing the contraction matrices for the homogeneous Riemann (or
boundary-Riemann) solutions. The extended Glimm-Goodman wave interaction
estimates are investigated for obtaining a stable scheme and positive gas
velocity, which matches the physical observation. The limit of approximation
solutions serves as an entropy solution of bounded variations. Moreover, the
range of the hydrodynamical region is also obtained.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci