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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2512.03378 |
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| _version_ | 1866915650964815872 |
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| author | Phiri, Moses Patson |
| author_facet | Phiri, Moses Patson |
| contents | 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 $L^{\infty}-$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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Bridging Analyticity and Sparseness in Hyperdissipative Navier-Stokes Systems Phiri, Moses Patson Analysis of PDEs Mathematical Physics 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 $L^{\infty}-$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. |
| title | On Bridging Analyticity and Sparseness in Hyperdissipative Navier-Stokes Systems |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2512.03378 |