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

Equation of motion for incompressible mixed fluid driven by evaporation and its application to online rankings