Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of weak solutions in the context of multidimensional
  incompressible fluid dynamics   We define the concept of energy-variational solutions for the Navier--Stokes
and Euler equations. The underlying relative energy inequality holds as an
equality for classical solutions and if the additional variable vanishes, these
solutions are equivalent to the weak formulation with the strong energy
inequality. By introducing an additional defect variable in time, all
restrictions and all concatenations of energy-variational solutions are again
energy-variational solutions. Via the criterion of maximal dissipation, a
unique solution is selected that is not only continuously depending on the data
but also turns out to be a unique weak solution.

28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex