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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 $L^\infty$ norm if the values of the energy and particle density are in the range of values where the corresponding equilibria contains a Dirac mass.
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X. Lu. The Boltzmann equation for Bose-Einstein particles: velocity concentration and convergence to equilibrium. J. Stat. Phys., 119, 1027-1067, (2005)
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M. Escobedo and J. J. L. Velázquez. Finite time blow-up for the bosonic Nordheim equation. Preprint
Cited in the paper.
C. Josserand, Y. Pomeau and S. Rica. Self-similar singularities in the kinetics of condensation. J. Low Temp. Phys. 145, 231-265, (2006)
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M. Escobedo, S. Mischler and J. J. L. Velázquez. On the fundamental solution of a linearized Uehling Uhlenbeck equation. Arch. Rat. Mech. Analysis, 186, 2, 309-349, (2007)
2007
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M. Escobedo, S. Mischler and J. J. L. Velázquez. Singular solutions for the Uehling Uhlenbeck equation. Proc. Royal Soc. Edinburgh. 138A, 67-107, (2008)
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X. Lu. The Boltzmann equation for Bose-Einstein particles: Condensation in finite time. J. Stat. Phys., 150, 1138Ð1176, (2013)
2013
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