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On Self-similar Solutions to Degenerate Compressible Navier–Stokes Equations

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Abstract

We study cavitating solutions to compressible Navier–Stokes equations with degenerate density-dependent viscosity. We consider two types of small radial solutions: forward self-similar (expanders), and backward self-similar (shrinkers). In the first case, we construct such solutions by a fixed-point argument. In the second case, we prove non-existence of such solutions using weighted energy estimates.

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Acknowledgements

P. Germain was partially supported by the NSF Grant DMS-1501019. T. Iwabuchi was supported by JSPS KAKENHI Grant 17H04824.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012-1185, USA

    Pierre Germain & Tristan Léger

  2. Mathematical Institute, Tohoku University, Sendai City, 980-8578, Japan

    Tsukasa Iwabuchi

Authors
  1. Pierre Germain
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  2. Tsukasa Iwabuchi
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  3. Tristan Léger
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Correspondence to Tristan Léger.

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Communicated by A. Ionescu

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Germain, P., Iwabuchi, T. & Léger, T. On Self-similar Solutions to Degenerate Compressible Navier–Stokes Equations. Commun. Math. Phys. 381, 1001–1030 (2021). https://doi.org/10.1007/s00220-020-03919-6

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  • DOI: https://doi.org/10.1007/s00220-020-03919-6

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