Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations

Communications in Mathematical Physics

Volumn 266, Issue 2, 2006, Pages 547-569

  Lin, Tai Chia ^a,b   Zhang, Ping ^c  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b NATIONAL CENTER FOR THEORETICAL SCIENCES   (Taiwan)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746215050     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0061-x     Document Type: Article

References (26)

1. Ao, P., Chui, S.T.: Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases. Phys. Rev. A 58, 4836-4840 (1998)
2. Beirao da Veiga, H.: On the barotropic motion of compressible perfect fluids. Ann. Sc. Norm. Sup. Pisa 8, 417-451 (1981)
3. Beirao da Veiga, H.: Data dependence in the mathematical theory of compressible inviscid fluids. Arch. Rat. Mech. Anal. 119, 109-127 (1992)
4. Brezis, H., Gallout, T.: Nonlinear Schrödinger evolution equations. Nonlinear Analysis, TMA 4, 677-681 (1980)
5. Esry, B.D., Greene, C.H.: Spontaneous spatial symmetry breaking in two-component Bose-Einstein condensates. Phys. Rev. A 59, 1457-1460 (1999)
6. Hasan, Z.R., Goble, D.F.: Effect of boundary conditions on finite Bose-Einstein assemblies. Phys. Rev. A 10(2), 618-624 (1974)
7. Grenier, E.: Semiclassical limit of the nonlinear Schrödinger equation in small time. Proc. Amer. Math. Soc. 126, 523-530 (1998)
8. Ginzburg, V.L., Pitaevskii, L.P.: Zh. Eksperim. Theor. Fys. 34, 1240 (1958)
9. [Sov. Phys. JETP 7, 858 (1958)]
10. Hall, D.S., Matthews, M.R., Ensher, J.R., Wieman, C.E., Cornell, E.A.: Dynamics of component separation in a binary mixture of Bose- Einstein condensates. Phys. Rev. Lett. 81, 1539-1542 (1998)
11. Kato, T.: Perturbation theory of linear operator. Berlin: Springer, 1980
12. Lin, F.H., Lin, T.C.:Vortices in two-dimensional Bose-Einstein condensates. In: Geometry and nonlinear partial differential equations, AMS/IP Stud. Adv. Math. 29, Amer. Math. Soc., Providence, RI, 2002 pp. 87-114
13. Lin, F.H., Xin, J.X.: On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation. Commun. Math. Phys. 200(2), 249-274 (1999)
14. Lin, F.H., Zhang, P.: Semiclassical limit of the Gross-Pitaevskii equation in an exterior domain. Arch. Rat. Mech. Anal. 179, 79-107 (2005)
15. Lions, P.L.: Mathematical Topics in Fluid Mechanics, Vol. 1, Incompressible Models, Lecture series in mathematics and its applications, V. 3, Oxford: Clarendon Press, 1996
16. Majda, A.: Compressible fluid flow and systems of conservation laws in several space variables. New York, Springer 1984
17. Nirenberg, L.: On elliptic partial differential equations. Ann. Sci. Norm. Sup. Pisa 13, 115-162 (1959)
18. Pérez-García, V.M., Konotop, V.V., Brazhnyi, V.A.: Feshbach resonance induced shock waves in Bose-Einstein condensates. Phys. Rev. Lett. 92, 220-403(1-4) (2004)
19. Pitaevskii, L., Stringari, S.: Bose-Einstein condensation. Oxford: Oxford univ. Press, 2003
20. Puel, M.: Convergence of the Schrödinger-Poisson system to the incompressible Euler equations. Comm. Partial Diff. Eqs. 27, 2311-2331 (2002)
21. Segal, I.: Nonlinear semi-groups. Ann. Math. 78, 339-364 (1963)
22. Sideris, T.C.: Formation of singularities in three-dimensional compressible fluids. Commun. Math. Phys. 101, 475-485 (1985)
23. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton, NJ: Princeton University Press 1970
24. Sulem, C., Sulem, P.L.: The nonlinear Schrödinger equation self-focusing and wave collapse. New York: Springer 1999
25. Timmermans, E.: Phase separation of Bose-Einstein condensates. Phys. Rev. Lett. 81, 5718-5721 (1998)
26. Zhang, P.: Wigner measure and the Semiclassical limit of Schrodinger-Poisson equations. SIAM J. Math. Anal. 34, 700-718 (2003)