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Dynamical Systems, Plasmas and Gravitation pp 56–61Cite as

A limiting case of averaging compactness lemmas motivated by the kinetic formulation of some classical systems of fluid mechanics

  • Plasma And Gravitation
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Part of the book series: Lecture Notes in Physics ((LNP,volume 518))

Abstract

We consider transport equations with a second member which is a full space derivative. This structure coresponds to numerous models of fluid dynamics and to the kinetic formulation of isentropic gas dynamics and, for the case of scalar conservation laws, averaging lemmas prove regularizing effects. We extend the averaging lemmas to second members which are a full space derivative. Our method uses Calderón-Zygmund theory.

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Authors and Affiliations

  1. Laboratoire d’analyse Numérique, Université P. et M. Curie, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Benoit Perthame

  2. Institut Universitaire de France, France

    Benoit Perthame

  3. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, 53706, Madison, WI, USA

    Panagiotis E. Souganidis

Authors
  1. Benoit Perthame
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  2. Panagiotis E. Souganidis
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Editor information

P. G. L. Leach S. E. Bouquet J.-L. Rouet E. Fijalkow

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© 1999 Springer-Verlag

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Perthame, B., Souganidis, P.E. (1999). A limiting case of averaging compactness lemmas motivated by the kinetic formulation of some classical systems of fluid mechanics. In: Leach, P.G.L., Bouquet, S.E., Rouet, JL., Fijalkow, E. (eds) Dynamical Systems, Plasmas and Gravitation. Lecture Notes in Physics, vol 518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105912

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  • DOI: https://doi.org/10.1007/BFb0105912

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  • Print ISBN: 978-3-540-65467-4

  • Online ISBN: 978-3-540-49251-1

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