What question did this study set out to answer?

This research aims to advance the understanding of Navier-Stokes regularity using a causal-geometric framework.

March 26, 2026Open Access

Causal–Geometric Fluid Dynamics: Discrete Harmonic Regularisation and Navier–Stokes Regularity

Key Points

This research aims to advance the understanding of Navier-Stokes regularity using a causal-geometric framework.
Introduced discrete harmonic pulses inspired by de Broglie concepts.
Developed a regularisation technique to suppress finite-time blowup.
Analyzed the macroscopic behavior of fluid dynamics under this regularisation.
Successfully maintained fluid dynamics while preventing singularities.
Yielded a modified Kolmogorov spectrum as a testable outcome.
Provided a grounded approach to turbulence analysis.

Abstract

A causal-geometric approach to Navier-Stokes regularity: using de Broglie-inspired discrete harmonic pulses to introduce a physically grounded regularisation that suppresses finite-time blowup while preserving macroscopic fluid dynamics and yielding a testable modified Kolmogorov spectrum. ------- Keywords: Navier–Stokes Regularity • Causal Geometry • Discrete Harmonic Pulses • Leray Weak Solutions • Turbulence • Kolmogorov Spectrum • Energy Cascade • High-Frequency Suppression • A Priori Estimates • Structural Regularization • Mathematical Physics • Incompressible Flow • Nonlinear PDE • De Broglie Framework • Non-local Topology • Open Science

Causal–Geometric Fluid Dynamics: Discrete Harmonic Regularisation and Navier–Stokes Regularity

Key Points

Abstract

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