No Finite-Time Singularity in Collapse-Regularized Navier-Stokes
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| Natura: | Recurso digital |
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2025
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| _version_ | 1866901158729089024 |
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| author | Low, Dunstan |
| author_facet | Low, Dunstan |
| contents | <p dir="auto"><strong>No Finite-Time Singularity in Collapse-Regularized Navier-Stokes</strong></p> <p dir="auto">The classical 3D incompressible Navier-Stokes equations predict infinite velocity gradients at sharp boundaries (e.g., corners), leading to finite-time singularities. We prove that, in the collapse-regularized framework of the Gravity as Collapse (GAC) model, the velocity gradient is globally bounded. Time is procedural ($d\tau = k, dC$, $k = \sqrt{\hbar G / c^5}$), and collapse density $\rho_C > 0$ is smooth. The realized velocity scales as $v \sim \sqrt{\rho_C} \cdot f(\tau)$, with $|f|_\infty < \infty$. Near a boundary, $\rho_C(r) = \rho_0 (1 - e^{-r/\lambda})$ yields $|\nabla \rho_C| \leq \rho_0 / \lambda < \infty$. Thus, $|\nabla v| \leq v_0 / \lambda < \infty$ for all finite $\tau$. This resolves the singularity paradox without ad hoc cutoffs. The result is falsifiable via mesoscopic fluid experiments and BMV/QGEM analogs.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17491482 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | No Finite-Time Singularity in Collapse-Regularized Navier-Stokes Low, Dunstan <p dir="auto"><strong>No Finite-Time Singularity in Collapse-Regularized Navier-Stokes</strong></p> <p dir="auto">The classical 3D incompressible Navier-Stokes equations predict infinite velocity gradients at sharp boundaries (e.g., corners), leading to finite-time singularities. We prove that, in the collapse-regularized framework of the Gravity as Collapse (GAC) model, the velocity gradient is globally bounded. Time is procedural ($d\tau = k, dC$, $k = \sqrt{\hbar G / c^5}$), and collapse density $\rho_C > 0$ is smooth. The realized velocity scales as $v \sim \sqrt{\rho_C} \cdot f(\tau)$, with $|f|_\infty < \infty$. Near a boundary, $\rho_C(r) = \rho_0 (1 - e^{-r/\lambda})$ yields $|\nabla \rho_C| \leq \rho_0 / \lambda < \infty$. Thus, $|\nabla v| \leq v_0 / \lambda < \infty$ for all finite $\tau$. This resolves the singularity paradox without ad hoc cutoffs. The result is falsifiable via mesoscopic fluid experiments and BMV/QGEM analogs.</p> |
| title | No Finite-Time Singularity in Collapse-Regularized Navier-Stokes |
| url | https://doi.org/10.5281/zenodo.17491482 |