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math.AP2018
Localised necessary conditions for singularity formation in the Navier-Stokes equations with curved boundary
Dallas Albritton, Tobias Barker
We generalize two results in the Navier-Stokes regularity theory whose proofs rely on `zooming in' on a presumed singularity to the local setting near a curved portion $Γ\subset \p…
math.AP2018
On local Type I singularities of the Navier-Stokes equations and Liouville theorems
Dallas Albritton, Tobias Barker
We prove that suitable weak solutions of the Navier-Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying…
math.AP2018
Global weak Besov solutions of the Navier-Stokes equations and applications
Dallas Albritton, Tobias Barker
We introduce a notion of global weak solution to the Navier-Stokes equations in three dimensions with initial values in the critical homogeneous Besov spaces $\dot{B}^{-1+\frac{3}{…