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On a Kinetic Equation for Coalescing Particles

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Abstract

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behaviour then rely on weak and strong compactness methods in L 1 in the spirit of the DiPerna-Lions theory for the Boltzmann equation.

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Authors and Affiliations

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

    Miguel Escobedo

  2. Mathématiques pour l’Industrie et la Physique, CNRS UMR 5640, Université Paul Sabatier–Toulouse 3, 118 route de Narbonne, 31062, Toulouse cedex 4, France

    Philippe Laurençot

  3. Laboratoire de Mathématiques Appliquées, Université de Versailles –, Saint Quentin, 45 avenue des Etats-Unis, 78035, Versailles, France

    Stéphane Mischler

  4. Projet BANG, INRIA Rocquencourt, B.P.105, 78153, Le Chesnay Cedex, France

    Stéphane Mischler

Authors
  1. Miguel Escobedo
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  2. Philippe Laurençot
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  3. Stéphane Mischler
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Correspondence to Stéphane Mischler.

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H.-.T. Yau

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Escobedo, M., Laurençot, P. & Mischler, S. On a Kinetic Equation for Coalescing Particles. Commun. Math. Phys. 246, 237–267 (2004). https://doi.org/10.1007/s00220-004-1037-3

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  • DOI: https://doi.org/10.1007/s00220-004-1037-3

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