Self-Similar Solutions to the Nonstationary Navier-Stokes Equations

Hao Jia (), Vladimir Šverák () and Tai-Peng Tsai ()
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Hao Jia: University of Minnesota, Institute for Advanced Studies, Princeton and Department of Mathematics
Vladimir Šverák: University of Minnesota, School of Mathematics
Tai-Peng Tsai: University of British Columbia, Department of Mathematics

Chapter 9 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 461-507 from Springer

Abstract: 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.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_9

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