Existence of a weak solution for the semigeostrophic equation with integrable initial data

Royal Society of Edinburgh - Proceedings A

Volumn 132, Issue 2, 2002, Pages 329-339

  Lopes Filho, M C ^a   Nussenzveig Lopes, H J ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036978676     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500001657     Document Type: Article

References (17)

1. R. Adams. Sobolev spaces. Pure and Applied Mathematics, vol. 65 (Academic, 1975).
2. J.-D. Benamou and Y. Brenier. Weak existence for the semigeostrophic equations formulated as a coupled Monge-Ampère/transport problem. SIAM J. Appl. Math. 58 (1998), 1450-1461.
3. C. Bennett and R. Sharpley. Interpolation of operators. Pure and Applied Mathematics, vol. 129 (Academic, 1988).
4. Y. Brenier. Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 64 (1991), 375-417.
5. D. Chae. Weak solutions of two-dimensional incompressible Euler equations. Nonlin. Analysis 23 (1994), 629-638.
6. M. J. P. Cullen and R. J. Douglas. Applications of the Monge-Ampère equation and Monge transport problem to meteorology and oceanography. Contemp. Math. 226 (1999), 33-53.
7. M. J. P. Cullen, J. Norbury, R. J. Purser and G. J. Shutts. Modelling the quasi-equilibrium dynamics of the atmosphere. Q. J. R. Meteor. Soc. 113 (1987), 735-757.
8. M. J. P. Cullen, J. Norbury and R. J. Purser. Generalized Lagrangian solutions for atmospheric and oceanic flows. SIAM J. Appl. Math. 51 (1991), 20-31.
9. J.-M. Delort. Existence de nappes de tourbillon en dimension deux. J. Am. Math. Soc. 4 (1991), 553-586.
10. R. DiPerna and A. Majda. Concentrations in regularizations for 2D incompressible flow. Commun. Pure Appl. Math. 60 (1987), 301-345.
11. L. C. Evans. Partial differential equations and Monge-Kantorovich mass transfer. In Current developments in mathematics, pp. 65-126 (Boston, MA: International Press, 1999).
12. B. J. Hoskins and F. P. Bretherton. Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 29 (1972). 11-37.
13. P. L. Lions. Mathematical topics in fluid mechanics. Incompressible models. Oxford Lecture Series in Mathematics and its Applications, vol. 3 (Oxford: Clarendon, 1996).
14. M. C. Lopes Filho, H. J. Nussenzveig Lopes and E. Tadmor. Approximate solutions of the incompressible Euler equations with no concentrations. Annls Inst. H. Poincaré Analyse Non Linéaire 17 (2000), 371-412.
15. A. Majda. Vorticity and the mathematical theory of incompressible fluid flow. Commun. Pure Appl. Math. 39 (1986), S187-S220.
16. A. B. Morgulis. On existence of two-dimensional nonstationary flows of an ideal incompressible liquid admitting a curl nonsummable to any power greater than 1. Siberian Math. J. 33 (1992), 934-937.
17. S. Schochet. The weak vorticity formulation of the 2D Euler equations and concentration-cancellation. Commun. PDEs 20 (1995), 1077-1104.