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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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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