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.
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Communicated by H. Spohn
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Escobedo, M., Velázquez, J.J.L. On the Blow Up and Condensation of Supercritical Solutions of the Nordheim Equation for Bosons. Commun. Math. Phys. 330, 331–365 (2014). https://doi.org/10.1007/s00220-014-2034-9
- Initial Data
- Weak Solution
- Mild Solution
- Einstein Condensate
- Dirac Mass