Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connections between Optimal Transport, Combinatorial Optimization and
  Hydrodynamics   There are well-established connections between combinatorial optimization,
optimal transport theory and Hydrodynamics, through the linear assignment
problem in combinatorics, the Monge-Kantorovich problem in optimal transport
theory and the model of inviscid, potential, pressure-less fluids in
Hydrodynamics. Here, we consider the more challenging quadratic assignment
problem (which is NP, while the linear assignment problem is just P) and find,
in some particular case, a correspondence with the problem of finding
stationary solutions of Euler's equations for incompressible fluids. For that
purpose, we introduce and analyze a suitable "gradient flow" equation.
Combining some ideas of P.-L. Lions (for the Euler equations) and
Ambrosio-Gigli-Savar\'e (for the heat equation), we provide for the initial
value problem a concept of generalized "dissipative" solutions which always
exist globally in time and are unique whenever theyare smooth.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con