Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-velocity hydrodynamics in fluid mechanics: Part II Existence of
  global $\kappa$-entropy solutions to compressible Navier-Stokes systems with
  degenerate viscosities   This paper addresses the issue of global existence of so-called
$\kappa$-entropy solutions to the Navier-Stokes equations for viscous
compressible and barotropic fluids with degenerate viscosities. We consider the
three dimensional space domain with periodic boundary conditions. Our solutions
satisfy the weak formulation of the mass and momentum conservation equations
and also a generalization of the BD-entropy identity called: $\kappa$-entropy.
This new entropy involves a mixture parameter $\kappa \in (0,1)$ between the
two velocities $\bf{u}$ and $\bf{u} + 2\nabla\varphi(\varrho)$ (the latter was
introduced by the first two authors in [C. R. Acad. Sci. Paris 2004]), where
$\bf{u}$ is the velocity field and $\varphi$ is a function of the density
$\varrho$ defined by $\varphi'(s)=\mu'(s)/s$. As a byproduct of the existence
proof, we show that two-velocity hydrodynamics (in the spirit of S.C. Shugrin
1994) is a possible formulation of a model of barotropic compressible flow with
degenerate viscosities. It is used in construction of approximate solutions
based on a conservative augmented approximate scheme.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th