Liouville-type theorems for the Navier–Stokes equations

An approach to the study of local regularity of weak solutions of the Navier–Stokes equations is described which is based on the reduction of questions of local smoothness of the original solutions to the proof of Liouville-type theorems for bounded ancient solutions of it. A survey is also given of results on Liouville theorems that are known at present for various classes of ancient solutions of the Navier–Stokes equations.
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