Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vortex solutions for the compressible Navier-Stokes equations with
  general viscosity coefficients in 1D: regularizing effects or not on the
  density   We consider Navier-Stokes equations for compressible viscous fluids in the
one-dimensional case with general viscosity coefficients. We prove the
existence of global weak solution when the initial momentum $\rho_0 u_0$
belongs to the set of the finite measure ${\cal M}(\mathbb{R})$ and when the
initial density $\rho_0$ is in the set of bounded variation functions
$BV(\mathbb{R})$. In particular it allows to deal with initial momentum which
are Dirac masses and initial density which admit shocks. We can observe in
particular that this type of initial data have infinite energy. Furthermore we
show that if the coupling between the density and the velocity is sufficiently
strong then the initial density which admits initially shocks is
instantaneously regularized and becomes continuous. This coupling is expressed
via the regularity of the so called effective velocity
$v=u+\frac{\mu(\rho)}{\rho^2}\partial_x \rho$ with $\mu(\rho)$ the viscosity
coefficient. Inversely if the coupling between the initial density and the
initial velocity is too weak (typically $\rho_0 v_0\in{\cal M}(\mathbb{R})$)
then we prove the existence of weak energy solution in finite time but the
density remains a priori discontinuous on the time interval of existence.

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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg