Ideal-Gas Approach to Hydrodynamics

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