On the blow up and condensation of supercritical solution of the Nordheim equation for bosons

M. Escobedo, J. J. L. Velázquez

Published 2012-10-05, updated 2014-01-20Version 3

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 $L^\infty$ norm if the values of the energy and particle density are in the range of values where the corresponding equilibria contains 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.