Rigorous derivation of the x-z semigeostrophic equations

Communications in Mathematical Sciences

Volumn 7, Issue 3, 2009, Pages 779-784

  Brenier, Yann ^a   Cullen, Mike ^b  

^a CNRS   (France)

^b MET OFFICE   (United Kingdom)

Author keywords

Asymptotic analysis; Navier Stokes equations; Semigeostrophic

Indexed keywords

EID: 70449088798     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2009.v7.n3.a13     Document Type: Article

References (13)

1. J.-D. Benamou, Y. Brenier, Weak existence for the semigeostrophic equations formulated as a coupled Monge - Ampere/transport problem, SIAM J. Appl. Math., 58, 1450-1461, 1998.
2. Y. Brenier, Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris I Math., 305, 805-808, 1987.
3. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math., 44, 375-417, 1991.
4. Y. Brenier, Remarks on the derivation of the hydrostatic Euler equations, Bull. Sci. Math., 127, 585-595, 2003.
5. A. Caffarelli, M. Milman (editors), Monge Ampère Equation: Applications to Geometry and Optimization, Contemporary Mathematics, 226, AMS 1999.
6. M. Cullen, M. Feldman, Lagrangian solutions of semigeostrophic equations in physical space, SIAM J. Math. Anal., 37, 1371-1395, 2006.
7. M. Cullen, W. Gangbo, A variational approach for the 2-D semi-geostrophic shallow water equations, Arch. Rat. Mech. Anal., 156, 241-273, 2006.
8. M. Cullen, R. Purser, An extended Lagrangian theory of semigeostrophic frontogenesis, J. Atmospheric Sci., 41, 1477-1497, 1984.
9. M. Cullen, J. Norbury, R. Purser, Generalised Lagrangian solutions for atmospheric and oceanic flows, SIAM J. Appl. Math., 51, 20-31, 1991.
10. M. Cullen, A Mathematical Theory of Large-scale Atmosphere/Ocean Flow, Imperial College Press, London, 2006.
11. B. Hoskins, The Geostrophic Momentum Approximation and the Semi-Geostrophic Equations, J. Atmospheric Sci., 32, 233-242, 1975.
12. G. Loeper, A fully nonlinear version of the incompressible Euler equations: the semigeostrophic system, SIAM J. Math. Anal., 38, 795-823, 2006.
13. C. Villani, Topics in Optimal Transportation,, American Mathematical Society, Providence, 2003.