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

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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 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.