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Viscous Compressible Flows Under Pressure

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Fluids Under Pressure

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

This chapter deals with the role of pressure in the theory of viscous compressible flows. The pressure state laws and viscosities are described. Special attention is devoted to non-monotone pressure laws and pressure dependent viscosities. The global existence proofs are discussed for approximate systems. Some relevant physical applications are described, including among others the anelastic Euler equations, shallow water model, granular media, or mixture problems.

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Acknowledgements

D. Bresch is partially supported by SingFlows project, grand ANR-18-CE40-0027. P.–E. Jabin is partially supported by NSF DMS Grants 161453, 1908739 and NSF Grant RNMS (Ki-Net) 1107444.

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Authors and Affiliations

  1. University of Savoie Mont Blanc, Le Bourget du Lac, France

    Didier Bresch

  2. University of Maryland, Maryland, MD, USA

    Pierre-Emmanuel Jabin

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  1. Didier Bresch
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Correspondence to Didier Bresch .

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Editors and Affiliations

  1. Department of Technical Mathematics, Czech Technical University, Prague, Czech Republic

    Tomáš Bodnár

  2. Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Giovanni P. Galdi

  3. Academy of Sciences of the Czech Republic, Prague, Czech Republic

    Šárka Nečasová

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Bresch, D., Jabin, PE. (2020). Viscous Compressible Flows Under Pressure. In: Bodnár, T., Galdi, G., Nečasová, Š. (eds) Fluids Under Pressure. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-39639-8_2

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