Local regularity theory for Navier-Stokes equations and Liouville type theorems

With Gregory Seregin, University of Oxford

Local regularity theory for Navier-Stokes equations and Liouville type theorems

In this expository talk, I would like to address a deep connection between the local regularity theory for the Navier-Stokes equations and existence or non-existence of non-trivial ancient ( backward) solutions to the Navier-Stokes system in the whole space.
In particular, it is explained that the existence of non-trivial so-called mild bounded ancient solutions, for which certain scale-invariant quantities are bounded, is the necessary and sufficient condition for the existence of suitable weak solutions that exhibit Type I blowups.

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