  We give a unique classical solution to initial value problem for a system of
partial differential equations for the densities of components of one
dimensional incompressible fluid mixture driven by evaporation. Motivated by
the known fact that the solution appears as an infinite particle limit of
stochastic ranking processes, which is a simple stochastic model of time
evolutions of e.g., Amazon Sales Ranks, we collected data from the web and
performed statistical fits to our formula. The results suggest that the fluid
equations and solutions may have an application in the analysis of online
rankings.
