Dynamic Interpolation and Higher-Order Turbulence Scales in 3D Navier-Stokes Flows
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.
Related
- Well-posedness of a stochastic Navier-Stokes system with dynamically coupled subgrid scales
- Concentration of Stationary Measures onto Large Scales in the Fast-Advection Limit of the Stochastically Forced Two-Dimensional Navier-Stokes Equations
- Spatial symmetry invariance of three-dimensional Navier-Stokes turbulence
- Reduction of Decaying Navier--Stokes Turbulence to the Quantum Pendulum
- Rigidity of Stationary Navier-Stokes Solutions with Transverse bound in Dimensions Five and Higher
BibTeX
@misc{phiri2026dynamic,
title = {{Dynamic Interpolation and Higher-Order Turbulence Scales in 3D Navier-Stokes Flows}},
author = {Moses Patson Phiri and Zoran Grujić},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33911},
eprint = {2610.33911},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33911},
}
RIS
TY - UNPB
TI - Dynamic Interpolation and Higher-Order Turbulence Scales in 3D Navier-Stokes Flows
AU - Moses Patson Phiri
AU - Zoran Grujić
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33911
UR - https://arxiv.org/abs/2610.33911
AB - 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.
ER -