Communications in Mathematical Physics

, Volume 330, Issue 1, pp 331–365 | Cite as

On the Blow Up and Condensation of Supercritical Solutions of the Nordheim Equation for Bosons

  • M. EscobedoEmail author
  • J. J. L. Velázquez


In this paper we prove that the solutions of the isotropic, spatially homogeneous Nordheim equation for bosons with bounded initial data blow up in finite time in the L norm if the values of the energy and particle density are in the range of values where the corresponding equilibria contain a Dirac mass. We also prove that, in the weak solutions, whose initial data are measures with values of particle and energy densities satisfying the previous condition, a Dirac measure at the origin forms in finite time.


Initial Data Weak Solution Mild Solution Einstein Condensate Dirac Mass 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad del País Vasco UPV/EHUBilbaoSpain
  2. 2.Basque Center for Applied Mathematics (BCAM)BilbaoSpain
  3. 3.Institute of Applied MathematicsUniversity of BonnBonnGermany

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