English

On Bridging Analyticity and Sparseness in Hyperdissipative Navier-Stokes Systems

Analysis of PDEs 2025-12-04 v1 Mathematical Physics math.MP

Abstract

We study the three-dimensional hyper-dissipative Navier-Stokes system in the near-critical regime below the Lions threshold. Leveraging a quantified analyticity-sparseness gap, we introduce a time-weighted bridge inequality across derivative levels and a focused-extremizer hypothesis capturing peak concentration at a fixed point. Together with a harmonic-measure contraction on one-dimensional sparse sets, these mechanisms enforce quantitative decay of high-derivative LL^{\infty}-norms and rule out blow-up. Under scale-refined, slowly varying time weights, solutions extend analytically past the prospective singular time, thereby refining the analyticity-sparseness framework, complementing recent exclusions of rapid-rate blow-up scenarios, and remaining consistent with recent non-uniqueness results.

Keywords

Cite

@article{arxiv.2512.03378,
  title  = {On Bridging Analyticity and Sparseness in Hyperdissipative Navier-Stokes Systems},
  author = {Moses Patson Phiri},
  journal= {arXiv preprint arXiv:2512.03378},
  year   = {2025}
}
R2 v1 2026-07-01T08:06:56.950Z