This erratum corrects the errors in the article ‘Hydrody- namics at the smallest scales: a solvability criterion for Navier-Stokes equations in high dimensions’. There are problems with lemmas 4.2 and 4.3, both which are central to the L1-based proof of the main theorem.
The above-mentioned article contains two proofs of the same theorem. Fortunately, the L2-based proof in §3 seems to be correct. We have not been able to find a rigorous way to fix the L1-based proof. Whether or not it can be fixed is an open problem which we wish to pose.
We are very grateful to Dr X.-J. Wang, currently at Pennsylvania State University, for finding the errors.
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