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

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 $L^{p,\infty }({\mathbb{R}}^3)$ with $p>\frac{3}{2}$.

22 pages

Cited by in corpus (3)

• On Wolf's regularity criterion of suitable weak solutions to the Navier-Stokes equations
• On local Type I singularities of the Navier-Stokes equations and Liouville theorems
• Liouville theorem of axially symmetric Navier-Stokes equations with growing velocity at infinity