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A Microscopic Point of View on Singularities in Fluid Models

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Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics

Part of the book series: Springer INdAM Series ((SINDAMS,volume 17))

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Abstract

These lecture notes present some challenging problems regarding the multiscale analysis of some systems exhibiting singularities at the macroscopic scale. We are interested namely in shocks for the compressible Euler equations in 1D, vortex sheets for the incompressible Euler equations in 2D, and spatial concentrations for the Boltzmann equation. We would like to obtain a microscopic description of these singularities, and to understand whether the scale separation is relevant.

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Authors and Affiliations

  1. Département de Mathématiques et Applications, Ecole Normale Supérieure & Université Pierre et Marie Curie, Paris 6, France

    Laure Saint-Raymond

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  1. Laure Saint-Raymond
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Correspondence to Laure Saint-Raymond .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Ferruccio Colombini

  2. Dipartimento di Matematica e Geoscienze, Università di Trieste, Trieste, Italy

    Daniele Del Santo

  3. Institut de Mathématiques de Bordeaux, Université de Bordeaux - UMR5251, Talence, France

    David Lannes

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Saint-Raymond, L. (2017). A Microscopic Point of View on Singularities in Fluid Models. In: Colombini, F., Del Santo, D., Lannes, D. (eds) Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics. Springer INdAM Series, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-52042-1_9

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