Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and formal stability criteria of spatially inhomogeneous
  stationary solutions to the Vlasov equation for the Hamiltonian mean-field
  model   Stability of spatially inhomogeneous solutions to the Vlasov equation is
investigated for the Hamiltonian mean-field model to provide the spectral
stability criterion and the formal stability criterion in the form of necessary
and sufficient conditions. These criteria determine stability of spatially
inhomogeneous solutions whose stability has not been decided correctly by using
a less refined formal stability criterion. It is shown that some of such
solutions can be found in a family of stationary solutions to the Vlasov
equation, which is parametrized with macroscopic quantities and has a two-phase
coexistence region in the parameter space.

6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int