The Primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations
| cam.issuedOnline | 2021-11-04 | |
| cam.orpheus.counter | 9 | |
| cam.orpheus.success | 2022-05-11: embargo success field applied | |
| dc.contributor.author | Li, Jinkai | |
| dc.contributor.author | Titi, Edriss | |
| dc.contributor.author | Yuan, Guozhi | |
| dc.contributor.orcid | Titi, Edriss [0000-0002-5004-1746] | |
| dc.date.accessioned | 2021-11-02T00:31:10Z | |
| dc.date.available | 2021-11-02T00:31:10Z | |
| dc.description.abstract | In this paper, we provide rigorous justification of the hydrostatic approximation and the derivation of primitive equations as the small aspect ratio limit of the incompressible three-dimensional Navier-Stokes equations in the anisotropic horizontal viscosity regime. Setting ε >0 to be the small aspect ratio of the vertical to the horizontal scales of the domain, we investigate the case when the horizontal and vertical viscosities in the incompressible three-dimensional Navier-Stokes equations are of orders O(1) and ε^α, respectively, with α>2, for which the limiting system is the primitive equations with only horizontal viscosity as ε tends to zero. In particular we show that for "well prepared" initial data the solutions of the scaled incompressible three-dimensional Navier-Stokes equations converge strongly, in any finite interval of time, to the corresponding solutions of the anisotropic primitive equations with only horizontal viscosities, as ε tends to zero, and that the convergence rate is of order O(ε^(β/2)), where β=min{α-2,2}. Note that this result is different from the case α=2 studied in [Li, J.; Titi, E.S.,The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: Rigorous justification of the hydrostatic approximation, J. Math. Pures Appl., Vol. 124, (2019), 30-58], where the limiting system is the primitive equations with full viscosities and the convergence is globally in time and its rate of order O(ε). | |
| dc.description.sponsorship | Einstein Stiftung/Foundation-Berlin, Einstein Visiting Fellowship No. EVF-2017-358. | |
| dc.identifier.doi | 10.17863/CAM.77616 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/330173 | |
| dc.language.iso | eng | |
| dc.publisher | Elsevier | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.title | The Primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations | |
| dc.type | Article | |
| dcterms.dateAccepted | 2021-10-26 | |
| prism.publicationName | Journal of Differential Equations | |
| rioxxterms.licenseref.startdate | 2021-10-28 | |
| rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
| rioxxterms.type | Journal Article/Review | |
| rioxxterms.version | AM | |
| rioxxterms.versionofrecord | 10.1016/j.jde.2021.10.048 |
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