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Models and Special Solutions of the Navier–Stokes Equations

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Abstract

Some aspects of the roles of exact solutions of the Navier–Stokes equations are considered with special emphasis on their well posedness. Many of them are classical examples, but they are looked at from a modern viewpoint of partial differential equations. Also considered are model equations describing motion of incompressible viscous fluid. Demonstrations are given for importance of both nonlinearity and nonlocality alike by mathematical analyses and numerical experiments.

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Acknowledgements

The author is partially supported by JSPS KAKENHI 24244007. Part of the present chapter was written while the author was a visitor in 2014 to School of Mathematics, University of Minnesota. He would like to express his deepest gratitude for its generous support to him.

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  1. Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan

    Hisashi Okamoto

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    Yoshikazu Giga

  2. Toulon, Var, France

    Antonin Novotny

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Okamoto, H. (2016). Models and Special Solutions of the Navier–Stokes Equations. In: Giga, Y., Novotny, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-10151-4_14-1

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