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On the Mathematical Theory of Fluid Dynamic Limits to Conservation Laws

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Advances in Mathematical Fluid Mechanics

Abstract

These lectures discuss topics in the theory of hyperbolic systems of conservation laws focusing on the mathematical theory of fluid-dynamic limits. First, we discuss the emergence of the compressible Euler equations for an ideal gas in the fluid-dynamic limit of the Boltzmann equation or of the BGK model. Then we survey the current state of the mathematical theory of fluid-dynamic limits for BGK systems and for discrete velocity models of relaxation type. This is done for the case that the limit is a scalar conservation law or a system of two equations.

In memory of John A. Nohel

Research partially supported dy the TMR porject HCL #ERBFNRXCT960033 and the National Science Foundation.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Athanasios E. Tzavaras

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  1. Athanasios E. Tzavaras
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Editors and Affiliations

  1. Mathematical Institute, Charles University, Sokolovská 83, 18675, Prague 8, Czech Republic

    Josef Málek , Jindřich Nečas  & Mirko Rokyta ,  & 

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115-2888, USA

    Jindřich Nečas

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© 2000 Springer-Verlag Berlin Heidelberg

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Tzavaras, A.E. (2000). On the Mathematical Theory of Fluid Dynamic Limits to Conservation Laws. In: Málek, J., Nečas, J., Rokyta, M. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57308-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-57308-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67786-4

  • Online ISBN: 978-3-642-57308-8

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