Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing viscosity as a selection principle for the Euler equations:
  The case of 3D shear flow   We show that for a certain family of initial data, there exist non-unique
weak solutions to the 3D incompressible Euler equations satisfying the weak
energy inequality, whereas the weak limit of every sequence of Leray-Hopf weak
solutions for the Navier-Stokes equations, with the same initial data, and as
the viscosity tends to zero, is uniquely determined and equals the shear flow
solution of the Euler equations. This simple example suggests that, also in
more general situations, the vanishing viscosity limit of the Navier-Stokes
equations could serve as a uniqueness criterion for weak solutions of the Euler
equations.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th