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.
Vasseur, A new proof of partial regularity of solutions to Navier–Stokes equations,Nonlinear Differential Equations and Applications14(2007), 753–785
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The paper establishes a coarse-grained resolution inequality Psi(r) <= 4 Psi^ell(r) + 4 Omega^ell(r) and a fixed-chain depletion theorem for combined pressure-flux work in the Navier-Stokes CKN setting.
The paper presents a conditional scale-critical defect-cascade reduction for the local regularity problem of the 3D incompressible Navier-Stokes equations that excludes invisible cascades to obtain CKN-scale regularity under structural hypotheses.
citing papers explorer
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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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Coarse-Grained Resolution and Pressure-Flux Work Depletion for Navier-Stokes CKN Badness
The paper establishes a coarse-grained resolution inequality Psi(r) <= 4 Psi^ell(r) + 4 Omega^ell(r) and a fixed-chain depletion theorem for combined pressure-flux work in the Navier-Stokes CKN setting.
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Invisible Defect Cascades for Navier-Stokes Regularity
The paper presents a conditional scale-critical defect-cascade reduction for the local regularity problem of the 3D incompressible Navier-Stokes equations that excludes invisible cascades to obtain CKN-scale regularity under structural hypotheses.