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dc.contributor.authorLin, Quyuan
dc.contributor.authorLiu, Xin
dc.contributor.authorTiti, Edriss
dc.date.accessioned2022-06-15T15:01:08Z
dc.date.available2022-06-15T15:01:08Z
dc.date.issued2022
dc.identifier.issn1422-6928
dc.identifier.others00021-022-00705-3
dc.identifier.other705
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/338121
dc.descriptionFunder: Deutsche Forschungsgemeinschaft; doi: http://dx.doi.org/10.13039/501100001659
dc.descriptionFunder: Simons Foundation; doi: http://dx.doi.org/10.13039/100000893
dc.description.abstractWe study the effect of the fast rotation and vertical viscosity on the lifespan of solutions to the three-dimensional primitive equations (also known as the hydrostatic Navier-Stokes equations) with impermeable and stress-free boundary conditions. Firstly, for a short time interval, independent of the rate of rotation | Ω | , we establish the local well-posedness of solutions with initial data that is analytic in the horizontal variables and only L 2 in the vertical variable. Moreover, it is shown that the solutions immediately become analytic in all the variables with increasing-in-time (at least linearly) radius of analyticity in the vertical variable for as long as the solutions exist. On the other hand, the radius of analyticity in the horizontal variables might decrease with time, but as long as it remains positive the solution exists. Secondly, with fast rotation, i.e., large | Ω | , we show that the existence time of the solution can be prolonged, with "well-prepared" initial data. Finally, in the case of two spatial dimensions with Ω = 0 , we establish the global well-posedness provided that the initial data is small enough. The smallness condition on the initial data depends on the vertical viscosity and the initial radius of analyticity in the horizontal variables.
dc.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectArticle
dc.subjectAnisotropic vertically viscous primitive equations
dc.subjectFast rotation
dc.subjectWell-posedness theory
dc.subjectHydrostatic Navier-Stokes equations
dc.subject35Q35
dc.subject35Q86
dc.subject86A10
dc.subject76E07
dc.titleOn the Effect of Fast Rotation and Vertical Viscosity on the Lifespan of the 3D Primitive Equations.
dc.typeArticle
dc.date.updated2022-06-15T15:01:07Z
prism.issueIdentifier3
prism.publicationNameJ Math Fluid Mech
prism.volume24
dc.identifier.doi10.17863/CAM.85530
dcterms.dateAccepted2022-05-30
rioxxterms.versionofrecord10.1007/s00021-022-00705-3
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidLin, Quyuan [0000-0002-7506-8232]
dc.contributor.orcidTiti, Edriss [0000-0002-5004-1746]
dc.identifier.eissn1422-6952
dc.publisher.urlhttp://dx.doi.org/10.1007/s00021-022-00705-3
pubs.funder-project-idEngineering and Physical Sciences Research Council (EP/R014604/1)
cam.issuedOnline2022-06-15


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