Abstract:In this short paper we prove the global regularity of solutions to the Navier-Stokes equations under the assumption that slightly supercritical quantities are bounded. As a consequence, we prove that if a solution u to the Navier-Stokes equations blows-up, then certain slightly supercritical Orlicz norms must become unbounded. This partially answers a conjecture recently made by Terence Tao. The proof relies on quantitative regularity estimates at the critical level and transfer of subcritical information on t… Show more
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