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2025
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| Online Access: | https://doi.org/10.2139/ssrn.5355152 |
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| author | Tao, Pan Yueyu, Pan |
| author_facet | Tao, Pan Yueyu, Pan |
| contents | <p>This paper focuses on the core problem of global smoothness of strong solutions to the 3D incompressible Navier-Stokes equations. By constructing a three-tier analytical framework of "constraint system-intrinsic configuration-reductio ad absurdum", it rigorously proves that under the constraints of initial data in , non-zero viscosity coefficient, and regular external force fields, strong solutions do not exhibit finite-time blowup, can be extended to the entire time axis, and maintain global smoothness. The study innovatively combines physical constraints (e.g., upper bounds of viscous stress in molecular kinetics, Kolmogorov scales in turbulence) with mathematical analysis (Sobolev space estimates, elliptic regularity theory), independently derives high-order regularity of the pressure field, and controls the singularity of nonlinear terms through optimized high-order energy estimates. The proof by contradiction shows that assuming blowup leads to contradictions with energy conservation, continuum axioms, and molecular kinetic theory, thus confirming the necessity of global smoothness. This research fills the gap in Navier-Stokes equation theory regarding "extension of local smooth solutions to global ones" and provides significant theoretical support for turbulent numerical simulation and engineering flow prediction.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_2139_ssrn_5355152 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Study on the Global Smoothness of Solutions to the Navier-Stokes Equations Tao, Pan Yueyu, Pan <p>This paper focuses on the core problem of global smoothness of strong solutions to the 3D incompressible Navier-Stokes equations. By constructing a three-tier analytical framework of "constraint system-intrinsic configuration-reductio ad absurdum", it rigorously proves that under the constraints of initial data in , non-zero viscosity coefficient, and regular external force fields, strong solutions do not exhibit finite-time blowup, can be extended to the entire time axis, and maintain global smoothness. The study innovatively combines physical constraints (e.g., upper bounds of viscous stress in molecular kinetics, Kolmogorov scales in turbulence) with mathematical analysis (Sobolev space estimates, elliptic regularity theory), independently derives high-order regularity of the pressure field, and controls the singularity of nonlinear terms through optimized high-order energy estimates. The proof by contradiction shows that assuming blowup leads to contradictions with energy conservation, continuum axioms, and molecular kinetic theory, thus confirming the necessity of global smoothness. This research fills the gap in Navier-Stokes equation theory regarding "extension of local smooth solutions to global ones" and provides significant theoretical support for turbulent numerical simulation and engineering flow prediction.</p> |
| title | Study on the Global Smoothness of Solutions to the Navier-Stokes Equations |
| url | https://doi.org/10.2139/ssrn.5355152 |