Please use this identifier to cite or link to this item:
https://olympias.lib.uoi.gr/jspui/handle/123456789/31859Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Konstantinos E. Kyritsis | en |
| dc.date.accessioned | 2022-07-20T08:52:00Z | - |
| dc.date.available | 2022-07-20T08:52:00Z | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/31859 | - |
| dc.identifier.uri | http://dx.doi.org/10.26268/heal.uoi.11674 | - |
| dc.rights | CC0 1.0 Universal | * |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.subject | Incompressible flows | en |
| dc.subject | Navier-Stokes equations | en |
| dc.subject | 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.type | report | el |
| heal.type.en | Technical Report | en |
| heal.type.el | Τεχνική αναφορά | el |
| heal.generalDescription | Abstract In this paper is presented 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 velocity 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.classification | MATHEMATICAL PHYSICS | - |
| heal.dateAvailable | 2022-07-20T08:53:01Z | - |
| heal.language | en | el |
| heal.access | free | el |
| heal.recordProvider | University of Iannina, School of Economic and Administrative Sciences, Dept of Accouning-Finance | en |
| heal.fullTextAvailability | true | - |
| Appears in Collections: | Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά) - ΛΧ | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Kyritsis_K_Νavier-Stokes_17_07_22.pdf | 1.14 MB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License
