Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence of finite energy weak solutions to the Quantum
  Navier-Stokes equations with non-trivial far-field behavior   We prove global existence of finite energy weak solutions to the quantum
Navier-Stokes equations in the whole space with non trivial far-field condition
in dimensions d = 2,3. The vacuum regions are included in the weak formulation
of the equations. Our method consists in an invading domains approach. More
precisely, by using a suitable truncation argument we construct a sequence of
approximate solutions. The energy and the BD entropy bounds allow for the
passage to the limit in the truncated formulation leading to a finite energy
weak solution. Moreover, the result is also valid in the case of compressible
Navier-Stokes equations with degenerate viscosity.

36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom