Formation of Singularities

  • Yves Pomeau
  • Minh-Binh Tran
Part of the Lecture Notes in Physics book series (LNP, volume 967)


This chapter is devoted to a rather detailed study of the dynamical transition of the state of a gas of bosons without condensate to a state with condensate, or equivalently to the dynamical formation of a condensate. This transition manifests itself as a finite time singularity of the solution of the Boltzmann– Nordheim kinetic equation at zero wavenumber. This singularity is described by a self-similar solution of this equation of the second kind in the terminology of Zelȉdovich [167].


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yves Pomeau
    • 1
  • Minh-Binh Tran
    • 2
  1. 1.LadHyXÉcole PolytechniquePalaiseau CedexFrance
  2. 2.Department of MathematicsSouthern Methodist UniversityDallasUSA

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