Archive for Rational Mechanics and Analysis

, Volume 143, Issue 1, pp 29-51

First online:

On Leray's Self‐Similar Solutions of the Navier‐Stokes Equations Satisfying Local Energy Estimates

  • Tai‐Peng TsaiAffiliated withSchool of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA; e‐::

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This paper proves that Leray's self‐similar solutions of the three‐dimensional Navier‐Stokes equations must be trivial under very general assumptions, for example, if they satisfy local energy estimates.