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

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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–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 \({p > \frac{3}{2}}\).

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Authors and Affiliations

  1. Department of Mathematics, Chung-Ang University, Seoul, 156-756, Republic of Korea

    Dongho Chae

  2. Department of Mathematics, Humboldt University Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Jörg Wolf

Authors
  1. Dongho Chae
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  2. Jörg Wolf
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Correspondence to Dongho Chae.

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Communicated by P. Constantin

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Chae, D., Wolf, J. On the Liouville Type Theorems for Self-Similar Solutions to the Navier–Stokes Equations. Arch Rational Mech Anal 225, 549–572 (2017). https://doi.org/10.1007/s00205-017-1110-7

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  • DOI: https://doi.org/10.1007/s00205-017-1110-7

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