The Ladder of Gaps Physics B: Post-Navier-Stokes Equations– Regularity Phase Transitions and the Hierarchy of Information Conservation
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2026
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| _version_ | 1866902103502356480 |
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>The millennium problem of global existence of smooth solutions to the Navier<br>Stokes equations has long been framed as a binary existence question. This paper<br>identifies three structural noises inherent in the problem’s formulation — the cult<br>of smooth solutions, the deterministic evolution framework, and the linear super<br>position assumption of classical function spaces — and transforms them into gen<br>erative seeds for new theoretical dimensions. By establishing a “hierarchy of infor<br>mation conservation strength” as the organizing principle, the concept of solution<br>is reconstructed as a multilevel phase-transition ladder ranging from Leray-Hopf<br>weak solutions, measure-valued solutions, randomized solutions, to coarse-grained<br>fields. Each level corresponds to a different strength of information conservation<br>and causal locality, and the regularity gap is no longer a question of existence of<br>smoothness but a critical threshold for phase transitions between levels. This paper<br>develops a dynamics of level transitions that includes order parameters, information<br>recombination operators, and irreversible entropy increase. It proves the complete<br>compatibility of this framework with the core results in the field: Leray’s global<br>existence, Caffarelli-Kohn-Nirenberg partial regularity, Tao’s averaged blowup con<br>struction, and Buckmaster-Vicol’s non-uniqueness of weak solutions. Quantitative<br>links are established with Kolmogorov turbulence scaling, Prandtl boundary layer<br>theory, and statistical mechanics phase transition theory. This framework shifts<br>the mathematical theory of the Navier-Stokes equations from the existence prob<br>lem of smooth solutions toward a hierarchical classification of solution concepts,<br>providing a self-consistent language for the multiscale structure of turbulence.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20390931 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | The Ladder of Gaps Physics B: Post-Navier-Stokes Equations– Regularity Phase Transitions and the Hierarchy of Information Conservation zhou, changzheng zhou, ziqing Navier-Stokes equations; regularity phase transition; hierarchy of information conservation; weak solution ladder; causal locality; level transition dynamics; turbulence <p>The millennium problem of global existence of smooth solutions to the Navier<br>Stokes equations has long been framed as a binary existence question. This paper<br>identifies three structural noises inherent in the problem’s formulation — the cult<br>of smooth solutions, the deterministic evolution framework, and the linear super<br>position assumption of classical function spaces — and transforms them into gen<br>erative seeds for new theoretical dimensions. By establishing a “hierarchy of infor<br>mation conservation strength” as the organizing principle, the concept of solution<br>is reconstructed as a multilevel phase-transition ladder ranging from Leray-Hopf<br>weak solutions, measure-valued solutions, randomized solutions, to coarse-grained<br>fields. Each level corresponds to a different strength of information conservation<br>and causal locality, and the regularity gap is no longer a question of existence of<br>smoothness but a critical threshold for phase transitions between levels. This paper<br>develops a dynamics of level transitions that includes order parameters, information<br>recombination operators, and irreversible entropy increase. It proves the complete<br>compatibility of this framework with the core results in the field: Leray’s global<br>existence, Caffarelli-Kohn-Nirenberg partial regularity, Tao’s averaged blowup con<br>struction, and Buckmaster-Vicol’s non-uniqueness of weak solutions. Quantitative<br>links are established with Kolmogorov turbulence scaling, Prandtl boundary layer<br>theory, and statistical mechanics phase transition theory. This framework shifts<br>the mathematical theory of the Navier-Stokes equations from the existence prob<br>lem of smooth solutions toward a hierarchical classification of solution concepts,<br>providing a self-consistent language for the multiscale structure of turbulence.</p> |
| title | The Ladder of Gaps Physics B: Post-Navier-Stokes Equations– Regularity Phase Transitions and the Hierarchy of Information Conservation |
| topic | Navier-Stokes equations; regularity phase transition; hierarchy of information conservation; weak solution ladder; causal locality; level transition dynamics; turbulence |
| url | https://doi.org/10.5281/zenodo.20390931 |