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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
Article

Abstract

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.

Keywords

Initial Data Weak Solution Mild Solution Einstein Condensate Dirac Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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