Archive for Rational Mechanics and Analysis

, Volume 225, Issue 1, pp 549–572

On the Liouville Type Theorems for Self-Similar Solutions to the Navier–Stokes Equations


DOI: 10.1007/s00205-017-1110-7

Cite this article as:
Chae, D. & Wolf, J. Arch Rational Mech Anal (2017) 225: 549. doi:10.1007/s00205-017-1110-7


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–Ru̇žička–Šverák and Tsai. Using a Liouville type theorem, we also remove a scenario of asymptotically self-similar blow-up for the Navier–Stokes equations with the profile belonging to \({L^{p, \infty} (\mathbb{R}^3)}\) with \({p > \frac{3}{2}}\).

Funding information

Funder NameGrant NumberFunding Note
National Research Foundation of Korea
  • 2016R1A2B3011647
Deutsche Forschungsgemeinschaft
  • WO1988/1-1; 612414

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsChung-Ang UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsHumboldt University BerlinBerlinGermany

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