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arXiv · 2610.33911

Dynamic Interpolation and Higher-Order Turbulence Scales in 3D Navier-Stokes Flows

Moses Patson Phiri·Zoran Grujić
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Abstract

We investigate the three-dimensional unforced Navier-Stokes equations through the interaction between spatial analyticity and the geometric sparseness of regions of intense fluid activity (i.e., regions where the fluid's motion varies sharply). Interpreting higher-order derivative ratios as turbulence scales, we introduce time-weighted bridge inequalities that quantify the relationship between lower- and higher-order derivative norms. The time weights give the derivative ratios greater flexibility while ensuring that the resulting lower bound on the radius of analyticity dominates the sparseness scale of the super-level sets, indicating that the flow has entered the dissipation regime. Combining this scale comparison with a harmonic-measure maximum principle on one-dimensional sparse sets yields a contraction in the relevant derivative norm, thereby excluding a class of strongly turbulent blow-up scenarios. Consequently, the strong solution extends analytically beyond the candidate blow-up time.

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Moses Patson Phiri, Zoran Grujić. 2026-10-24. Dynamic Interpolation and Higher-Order Turbulence Scales in 3D Navier-Stokes Flows. https://arxiv.org/abs/2610.33911

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