Equation of Motion for Incompressible Mixed Fluid Driven by Evaporation and Its Application to Online Rankings

Kumiko Hattori, Tetsuya Hattori

Research output: Contribution to journalArticle

6 Citations (Scopus)


We consider a system of partial differential equations for the densities of components of one dimensional incompressible fluid mixture whose motion is driven by evaporation. We prove existence and give explicit form of unique global classical non-negative solution to initial value problem for the system. The solution is known to be an infinite particle limit of stochastic ranking processes, which is a simple stochastic model of time evolutions of Amazon Sales Ranks. As a practical appli cation, we collected data from the web and performed statistical fits to our formula. The results suggest that the system of equations and solutions, though very simple, may have applications in the analysis of online rankings.

Original languageEnglish
Pages (from-to)301-319
Number of pages19
JournalFunkcialaj Ekvacioj
Issue number3
Publication statusPublished - 2009 Jan 1



  • Evaporation driven fluid
  • Long tail
  • Non-linear wave
  • Online ranking
  • Stochastic ranking process

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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