Under a fixed scale-invariant bound on suitable weak solutions of 3D Navier-Stokes, smallness of the vertical velocity component yields a positive lower bound on the local regularity radius via harmonic pressure approximation.
Struwe, On partial regularity results for the Navier–Stokes equations,Com- munications on Pure and Applied Mathematics41(1988), no
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Establishes Liouville-type theorems for stationary fractional Navier-Stokes in R^n under integrability and large-scale Morrey energy bounds, with corollary for finite fractional energy when n/3 ≤ α < (n+2)/3.
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Finite-Scale One-Component Regularity via Harmonic Pressure for the 3D Navier-Stokes Equations
Under a fixed scale-invariant bound on suitable weak solutions of 3D Navier-Stokes, smallness of the vertical velocity component yields a positive lower bound on the local regularity radius via harmonic pressure approximation.
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Liouville-type theorems for the stationary fractional Navier-Stokes equations in $\mathbb{R}^n$
Establishes Liouville-type theorems for stationary fractional Navier-Stokes in R^n under integrability and large-scale Morrey energy bounds, with corollary for finite fractional energy when n/3 ≤ α < (n+2)/3.