### 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.

Original language | English (US) |
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Title of host publication | Handbook of Mathematical Analysis in Mechanics of Viscous Fluids |

Publisher | Springer International Publishing |

Pages | 461-507 |

Number of pages | 47 |

ISBN (Electronic) | 9783319133447 |

ISBN (Print) | 9783319133430 |

DOIs | |

State | Published - Apr 19 2018 |

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## Cite this

Jia, H., Sverak, V., & Tsai, T. P. (2018). Self-similar solutions to the nonstationary. In

*Handbook of Mathematical Analysis in Mechanics of Viscous Fluids*(pp. 461-507). Springer International Publishing. https://doi.org/10.1007/978-3-319-13344-7_9