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dc.contributor.authorLi, Jinkai
dc.contributor.authorTiti, Edriss
dc.contributor.authorYuan, Guozhi
dc.description.abstractIn 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.sponsorshipEinstein Stiftung/Foundation-Berlin, Einstein Visiting Fellowship No. EVF-2017-358.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.titleThe Primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations
prism.publicationNameJournal of Differential Equations
dc.contributor.orcidTiti, Edriss [0000-0002-5004-1746]
rioxxterms.typeJournal Article/Review
cam.orpheus.success2022-05-11: embargo success field applied

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Attribution-NonCommercial-NoDerivatives 4.0 International
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial-NoDerivatives 4.0 International