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Exact solutions of the Navier-Stokes equations via Leray’s scheme

Abstract

J. Leray considered a backward self-similar solution of the Navier-Stokes equations in the hope that it gives us an example of the finite-time blow-up of the three dimensional nonstationary Navier-Stokes equations. However, he showed no example of solutions. We list here some particular solutions and discuss their fluid mechanical properties. We also consider a forward self-similar solution, which describes solutions decaying as time tends to infinity.

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Okamoto, H. Exact solutions of the Navier-Stokes equations via Leray’s scheme. Japan J. Indust. Appl. Math. 14, 169 (1997). https://doi.org/10.1007/BF03167263

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  • DOI: https://doi.org/10.1007/BF03167263

Key words

  • Navier-Stokes equations
  • exact self-similar solutions