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Finite time blow-up and condensation for the bosonic Nordheim equation

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Abstract

The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of classical solutions of the homogeneous bosonic Nordheim equation that blow up in finite time. We also prove finite time condensation for a class of weak solutions of the kinetic equation.

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Acknowledgments

This work has been supported by DGES Grant 2011-29306-C02-00, Basque Government Grant IT641-13, the Hausdorff Center for Mathematics of the University of Bonn and the Collaborative Research Center The Mathematics of Emergent Effects (DFG SFB 1060, University of Bonn). The authors thank the hospitality of the Isaac Newton Institute of the University of Cambridge where this work was begun.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del País Vasco UPV/EHU, Apartado 644, 48080 , Bilbao, Spain

    M. Escobedo

  2. Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, 48009 , Bilbao, Spain

    M. Escobedo

  3. Institute of Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 , Bonn, Germany

    J. J. L. Velázquez

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  1. M. Escobedo
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  2. J. J. L. Velázquez
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Correspondence to M. Escobedo.

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Escobedo, M., Velázquez, J.J.L. Finite time blow-up and condensation for the bosonic Nordheim equation. Invent. math. 200, 761–847 (2015). https://doi.org/10.1007/s00222-014-0539-7

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  • DOI: https://doi.org/10.1007/s00222-014-0539-7

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