A simple global model for the general circulation of the atmosphere

Lions, J. L.; Témam, Roger; Wang, Shouhong

doi:10.1002/(sici)1097-0312(199708)50:8<707::aid-cpa1>3.0.co;2-a

Cited by 13 publications

(3 citation statements)

References 26 publications

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“…We refer to [17] and [31] for a physical discussion of these models and to [37] for some formal asymptotic expansions. We also refer to Lions, Temam, and Wang [23,24,25,26] for a more mathematical discussion and for some open mathematical problems.…”

Section: Introductionmentioning

confidence: 99%

Ekman layers of rotating fluids: The case of general initial data

Masmoudi

2000

Comm. Pure Appl. Math.

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Section: Introductionmentioning

confidence: 99%

Ekman layers of rotating fluids: The case of general initial data

Masmoudi

2000

Comm. Pure Appl. Math.

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“…For general "primitive" equations of geophysics, following methods for hyperbolic Euler-type systems of Bardos [17], Bourgeois and Beale [19] have demonstrated convergence to quasi-geostrophic limit equations for special classes of initial data (of infinite codimension). Lions, Temam and Wang have analyzed the viscous equations (1.1-1.2) in a series of seminal papers [37,38], while restricting to "prepared" initial conditions or conditional regularity hypotheses.…”

Section: Introductionmentioning

confidence: 99%

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

2000

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Abstract. Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear "2 1 2 dimensional" limit equations for N → +∞; smoothness assumptions are the same as for local existence theorems, that is initial data in Hα, α ≥ 3/4. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D "primitive" Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit resonant equations and convergence theorems.Mathematics Subject Classification. 76D05, 76D50, 76U05, 86A10.

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“…The study of the primitive equations was initiated by Lions, Wang, and Temam [31][32][33], who provided the mathematical setting for the equations and established results pertaining to the existence of weak and strong solutions. This theory was advanced by Temam and Ziane [51], who proved the existence of a global weak and the local strong solution (cf.…”

Section: Introductionmentioning

confidence: 99%

Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

Kukavica

Lombardo

Sammartino

2016

Arch Rational Mech Anal

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The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be O( √ ν). The main assumption is spatial analyticity of the initial datum.

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A simple global model for the general circulation of the atmosphere

Cited by 13 publications

References 26 publications

Ekman layers of rotating fluids: The case of general initial data

Ekman layers of rotating fluids: The case of general initial data

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

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