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Other literature type . 2026
License: CC BY
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ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
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Paper 150N: Fragmentation, Scale-Local, and Complement Control for High-Vorticity Navier–Stokes Amplification

Authors: Sarnowski, Michael;

Paper 150N: Fragmentation, Scale-Local, and Complement Control for High-Vorticity Navier–Stokes Amplification

Abstract

The paper formulates control targets for these channels using only classical Navier-Stokes quantities: vorticity, strain, positive stretching, enstrophy, dissipation, filtered support, component structure, and threshold weights. Fragmentation is treated as positive stretching distributed across multiple moving, reconnecting, or intermittently active components. Scale-local visibility is treated as positive stretching that appears only after filtering or scale decomposition. Complement stretching is treated as positive stretching outside a chosen high-vorticity mask, near a threshold band, or inside the complement of a smooth threshold weight. The main target is to show that the combined remaining ordinary-channel contribution is bounded by dissipation and lower-order enstrophy, either pointwise or in a subinterval-stable integrated form. The paper emphasizes that integrated estimates must control every intermediate time, not merely a full interval average. It also requires no double-counting among overlapping channels and a positive dissipation margin after coherent-channel control, remaining ordinary-channel control, and residual pathological-channel control are all included. Paper 150N does not prove unconditional Navier-Stokes regularity. Instead, it completes the ordinary-channel bridge map at the theorem-target level. Its conclusion is conditional: fragmentation, scale-locality, and complement stretching must either pay cost, become lower-order, transition to another named channel, or become residual pathology. The paper also identifies key failure modes, including reconnection without gradient cost, divergent scale budgets, nonsummable threshold flicker, margin exhaustion, hidden integrated spikes, and numerical overinterpretation. These failure modes define the next analytic tasks for residual pathological refinement, coefficient recovery, and final bridge assembly.

Keywords

Navier-Stokes equations; vorticity; enstrophy; vortex stretching; high-vorticity pinching; fragmentation; scale-local analysis; threshold complement; positive stretching; dissipation margin; channel decomposition; finite-budget control; residual pathology; regularity problem; classical fluid mechanics.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average