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The aim is to present a new theoretical framework for understanding fluid behavior using non-temporal principles.

April 30, 20260 citationsOpen Access

Non-Temporal Fluid Structural Theory

Key Points

The aim is to present a new theoretical framework for understanding fluid behavior using non-temporal principles.
Introduces Non-Temporal Fluid Structural Theory (NFT) and Temporal Projection Model (TPM)
Analyzes fluid flow as a structural recursion within a non-temporal equilibrium
Establishes a theorem connecting NFT to Navier–Stokes equations.
Reinterprets fluid flow not as a temporal process but as a self-sustaining structure
Establishes a structural correspondence between NFT and the Navier–Stokes system
Suggests that if NFT's convergence holds, regular solutions to Navier–Stokes equations are necessary.

Abstract

This paper presents the Non-Temporal Fluid Structural Theory (NFT) and its extension through the Temporal Projection Model (TPM), offering a structural reinterpretation of fluid motion and the Navier–Stokes equations. NFT reconceives fluid flow not as a process unfolding through time but as a self-sustaining structural recursion within a non-temporal equilibrium field. The Temporal Projection Model reintroduces time as a coordinate-level transformation of non-temporal recursion rather than as a fundamental physical variable. Through this projection, the NFT structural equilibrium is shown to correspond directly to the continuity and momentum equations of the Navier–Stokes system. The central result is a structural correspondence theorem: if NFT's recursive convergence holds globally, smooth and globally regular solutions to the Navier–Stokes equations follow as a structural necessity. This reframes the conditions of fluid regularity from temporal analysis to structural convergence theory. Related updates may be available at: patreon.com/NMStructuralTheoryLab

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