Mean field limit of a dynamical model of polymer systems

Weinan E, Hao Shen

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4 Scopus citations


This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations (SPDEs). We show that the mean field limit as N → ∞ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.

Original languageEnglish (US)
Pages (from-to)2591-2598
Number of pages8
JournalScience China Mathematics
Issue number12
StatePublished - Dec 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • McKean-Vlasov equation
  • mean field limit
  • polymers
  • stochastic PDEs


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