  Transport is one of the most important physical processes in all energy and
length scales. Ideal gases and hydrodynamics are, respectively, two opposite
limits of transport. Here, we present an unexpected mathematical connection
between these two limits; that is, there exist situations that the solution to
a class of interacting hydrodynamic equations with certain initial conditions
can be exactly constructed from the dynamics of noninteracting ideal gases. We
analytically provide three such examples. The first two examples focus on
scale-invariant systems, which generalize fermionization to the hydrodynamics
of strongly interacting systems, and determine specific initial conditions for
perfect density oscillations in a harmonic trap. The third example recovers the
dark soliton solution in a one-dimensional Bose condensate. The results can
explain a recent puzzling experimental observation in ultracold atomic gases by
the Paris group and make further predictions for future experiments. We
envision that extensive examples of such an ideal-gas approach to hydrodynamics
can be found by systematical numerical search, which can find broad
applications in different problems in various subfields of physics.
