  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.
