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arXiv · 1609.06962

On the Liouville type theorems for self-similar solutions to the Navier-Stokes equations

Dongho Chae·Joerg Wolf
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Abstract

We prove Liouville type theorems for the self-similar solutions to the Navier-Stokes equations. One of our results generalizes the previous ones by Nečas-Ružička-Šverak and Tsai. Using the Liouville type theorem we also remove a scenario of asymtotically self-similar blow-up for the Navier-Stokes equations with the profile belonging to $L^{p, \infty} (\Bbb R^3)$ with $p> \frac{3}{2}$.

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Dongho Chae, Joerg Wolf. 2016-09-22. On the Liouville type theorems for self-similar solutions to the Navier-Stokes equations. https://doi.org/10.1007/s00205-017-1110-7

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