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March 30, 20260 citationsOpen Access

Navier–Stokes Equations as Stability and Breakdown of Admissible Structure: A Structural Placement within the Paton System

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APAndrew John Paton

Key Points

  • The paper aims to clarify the structural role of the Navier–Stokes equations in the Paton System.
  • Interpreting the Navier–Stokes equations without introducing new physical laws.
  • Analyzing stability and breakdown in systems under constraint-driven flow.
  • Navier–Stokes equations describe the boundary between stable persistence and instability.
  • Turblence is framed as structural breakdown rather than randomness.

Abstract

This paper clarifies the structural role of the Navier–Stokes equations within the Paton System. Without introducing new physical laws or attempting to solve the equations, they are interpreted as describing the stability and breakdown of admissible structure under constraint-driven flow. Rather than representing fluid motion alone, the equations are placed as defining the boundary between stable persistence and instability within evolving systems. This interpretation resolves ambiguity surrounding turbulence by framing it as structural breakdown rather than randomness, while remaining fully consistent with established physical formalism.

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Cite This Study

Andrew John Paton (2026) studied this question.

synapsesocial.com/papers/69c9c51bf8fdd13afe0bcf90https://doi.org/10.5281/zenodo.19278521
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