# Self-similar solutions to the Navier-Stokes equations: a survey of recent results.

@article{Bradshaw2018SelfsimilarST, title={Self-similar solutions to the Navier-Stokes equations: a survey of recent results.}, author={Zachary Bradshaw and Tai-Peng Tsai}, journal={arXiv: Analysis of PDEs}, year={2018} }

We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].

#### 3 Citations

Local Energy Solutions to the Navier-Stokes Equations in Wiener Amalgam Spaces

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2021

Solutions in a scale of classes weaker than the finite energy Leray class and stronger than the infinite energy Lemari\'e-Rieusset class are established and help identify scalings at which certain properties may break down. Expand

Time-Global Regularity of the Navier-Stokes System with Hyper-Dissipation--Turbulent Scenario.

- Physics, Mathematics
- 2020

The question of whether the hyper-dissipative Navier-Stokes (NS) system can exhibit spontaneous formation of singularities in the super-critical regime--the hyper-dissipation being generated by a… Expand

Beyond Kolmogorov cascades

- Physics
- Journal of Fluid Mechanics
- 2019

The large-scale structure of many turbulent flows encountered in practical situations such as aeronautics, industry, meteorology is nowadays successfully computed using the Kolmogorov–Kármán–Howarth… Expand

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