A Short and Simple Solution of the Millennium Problem about the Navier-Stokes Equations and Similarly for the Euler Equations
| dc.contributor.author | Konstantinos E. Kyritsis | en |
| dc.date.accessioned | 2022-08-31T10:14:33Z | |
| dc.date.available | 2022-08-31T10:14:33Z | |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/31906 | |
| dc.identifier.uri | http://dx.doi.org/10.26268/heal.uoi.11721 | |
| dc.rights | CC0 1.0 Universal | * |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.subject | Navier-Stokes equations | en |
| dc.subject | Incompressible flows | en |
| dc.subject | Euler Equations | en |
| dc.subject | Clay Millennium Problem | en |
| dc.subject | Regularity | en |
| dc.subject | Blow-up | en |
| dc.title | A Short and Simple Solution of the Millennium Problem about the Navier-Stokes Equations and Similarly for the Euler Equations | en |
| heal.abstract | This paper presents a very short solution to the 4th Millennium problem about the Navier-Stokes equations. The solution proves that there cannot be a blow up in finite or infinite time, and the local in time smooth solutions can be extended for all times, thus regularity. This happily is proved not only for the Navier-Stokes equations but also for the inviscid case of the Euler equations both for the periodic or non-periodic formulation and without external forcing (homogeneous case). The proof is based on an appropriate modified extension in the viscous case of the well-known Helmholtz-Kelvin-Stokes theorem of invariance of the circulation of ve-locity in the Euler inviscid flows. This is essentially a 1D line density of (rotatory) momentum conservation. We discover a similar 2D surface density of (rotatory) momentum conservation. These conservations are indispensable, besides to the ordinary momentum conservation, to prove that there cannot be a blow-up in finite time, of the point vorticities, thus regularity. | en |
| heal.access | free | el |
| heal.bibliographicCitation | Kyritsis, K. (2022) A Short and Simple Solution of the Millennium Problem about the Navier-Stokes Equations and Similarly for the Euler Equations. Journal of Applied Mathematics and Physics, 10, 2538-2560. doi: 10.4236/jamp.2022.108172. | en |
| heal.classification | Mathematical Physics | |
| heal.dateAvailable | 2022-08-31T10:15:34Z | |
| heal.fullTextAvailability | true | |
| heal.identifier.secondary | 10.4236/jamp.2022.108172 | el |
| heal.journalName | Journal of Applied Mathematics and Physics | en |
| heal.journalType | peer-reviewed | el |
| heal.language | en | el |
| heal.publicationDate | 2022-08-31 | |
| heal.publisher | Scientific Research | en |
| heal.recordProvider | University of Iannina, School of Economic and Administrative Sciences, Dept of Accouning-Finance | en |
| heal.type | journalArticle | el |
| heal.type.el | Άρθρο περιοδικού | el |
| heal.type.en | Journal article | en |
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