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Self-Similar Solutions to the Nonstationary Navier-Stokes Equations

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Abstract

The Navier-Stokes equations have a natural scaling invariance which has played an essential role in their study. Valuable insights can be obtained from special solutions which are scale invariant with respect to the natural scaling. These solutions are often called self-similar solutions. In this chapter, important results for both forward self-similar and backward self-similar solutions are reviewed, and open problems will be mentioned.

The research of H.J is supported in part by grant DMS-1600779, and DMS-1128155 through IAS.

The research of VS was supported in part by grants DMS 1362467 and DMS 1159376 from the National Science Foundation. The research of TT was supported in part by the Natural Sciences and Engineering Research Council of Canada grant 261356-13.

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Author information

Authors and Affiliations

  1. Institute for Advanced Studies, Princeton and Department of Mathematics, University of Minnesota, 206 Church St. SE, 55455, Chicago, IL, USA

    Hao Jia

  2. School of Mathematics, University of Minnesota, Vincent Hall 236, 206 Church St. SE, 55455, Minneapolis, MN, USA

    Vladimir Šverák

  3. Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada

    Tai-Peng Tsai

Authors
  1. Hao Jia
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  2. Vladimir Šverák
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  3. Tai-Peng Tsai
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Correspondence to Hao Jia .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan

    Yoshikazu Giga

  2. Université de Toulon IMATH, Toulon, France

    Antonín Novotný

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Jia, H., Šverák, V., Tsai, TP. (2018). Self-Similar Solutions to the Nonstationary Navier-Stokes Equations. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_9

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