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.
Lin, A new proof of the Caffarelli–Kohn–Nirenberg theorem,Comm
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Establishes a finite-scale estimate for filtered vortex stretching in 3D Navier-Stokes bounded by vorticity direction defects, absorbed by filtered diffusion, with far-field and commutator terms controlled via Carleson embeddings and cylindrical Young measures.
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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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Filtered Vortex Stretching and Subgrid Defects for the Three-Dimensional Navier-Stokes Equations
Establishes a finite-scale estimate for filtered vortex stretching in 3D Navier-Stokes bounded by vorticity direction defects, absorbed by filtered diffusion, with far-field and commutator terms controlled via Carleson embeddings and cylindrical Young measures.