메뉴 건너뛰기




Volumn 32, Issue 3, 2012, Pages 709-715

On the cauchy problem for nonlinear schrödinger equations with rotation

Author keywords

Bose Einstein condensation; Fiangular momentum operator; Finite time blow up.; Nonlinear Schr dinger equation; Rotation

Indexed keywords


EID: 84859541270     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2012.32.703     Document Type: Article
Times cited : (46)

References (26)
  • 2
    • 61549128689 scopus 로고    scopus 로고
    • On the finite energy weak solutions to a system in quantum uid dynamics
    • P. Antonelli and P. Marcati, On the finite energy weak solutions to a system in quantum uid dynamics, Comm. Math. Phys., 287 (2009), 657-686.
    • (2009) Comm. Math. Phys. , vol.287 , pp. 657-686
    • Antonelli, P.1    Marcati, P.2
  • 3
    • 79551476770 scopus 로고    scopus 로고
    • On the regularization mechanism for the periodic korteweg-de vries equation comm
    • A. V. Babin, A. A. Ilyin and E. S. Titi, On the regularization mechanism for the periodic Korteweg-de Vries equation, Comm. Pure Applied Math., 64 (2011), 591-648.
    • (2011) Pure Applied Math. , vol.64 , pp. 591-648
    • Babin, A.V.1    Ilyin, A.A.2    Titi, E.S.3
  • 4
    • 33745667769 scopus 로고    scopus 로고
    • Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation
    • DOI 10.1137/050629392
    • W. Bao, Q. Du and Y. Z. Zhang, Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation, SIAM J. Appl. Math., 66 (2006), 758-786. (Pubitemid 43966547)
    • (2006) SIAM Journal on Applied Mathematics , vol.66 , Issue.3 , pp. 758-786
    • Bao, W.1    Du, Q.2    Zhang, Y.3
  • 5
    • 1542282092 scopus 로고    scopus 로고
    • Nonlinear schrödinger equations with repulsive harmonic potential and applications
    • R. Carles, Nonlinear Schrödinger equations with repulsive harmonic potential and applications, SIAM J. Math. Anal., 35 (2003), 823-843.
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 823-843
    • Carles, R.1
  • 6
    • 23844511635 scopus 로고    scopus 로고
    • Global existence results for nonlinear Schrödinger equations with quadratic potentials
    • R. Carles, Global existence results for nonlinear Schrödinger equations with quadratic potentials, Discrete Contin. Dyn. Syst., 13 (2005), 385-398. (Pubitemid 41179944)
    • (2005) Discrete and Continuous Dynamical Systems , vol.13 , Issue.2 , pp. 385-398
    • Carles, R.1
  • 7
    • 79961221521 scopus 로고    scopus 로고
    • Nonlinear schrödinger equation with time dependent potential
    • R. Carles, Nonlinear Schrödinger equation with time dependent potential, Commun. Math. Sci., 9 (2011), no. 4, 937-964.
    • (2011) Commun. Math. Sci. , vol.9 , Issue.4 , pp. 937-964
    • Carles, R.1
  • 8
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear schrödinger equations
    • New York University Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence, RI
    • T. Cazenave, "Semilinear Schrödinger Equations," Courant Lecture Notes in Mathematics, 10, New York University Courant Institute of Mathematical Sciences, New York, American Mathematical Society, Providence, RI, 2003.
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 9
    • 0001082862 scopus 로고    scopus 로고
    • Bose-Einstein Condensates in an Optical Lattice
    • D. Choi and Q. Niu, Bose-Einstein condensates in an optical lattice, Phys. Rev. Lett., 82 (1999), 2022-2025. (Pubitemid 129580682)
    • (1999) Physical Review Letters , vol.82 , Issue.10 , pp. 2022-2025
    • Choi, D.-I.1    Niu, Q.2
  • 10
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the cauchy problem for nonlinear schrödinger equations
    • R. T. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys., 18 (1977), 1794-1797.
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassey, R.T.1
  • 11
    • 41149168071 scopus 로고    scopus 로고
    • Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term
    • DOI 10.1002/mma.931
    • C. Hao, L. Hsiao and H.-L. Li, Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term, Math. Methods Appl. Sci., 31 (2008), 655-664. (Pubitemid 351427969)
    • (2008) Mathematical Methods in the Applied Sciences , vol.31 , Issue.6 , pp. 655-664
    • Hao, C.1    Hsiao, L.2    Li, H.-L.3
  • 12
    • 36148968128 scopus 로고    scopus 로고
    • Global well-posedness for the gross-pitaevskii equation with an angular momentum rotational term in three dimensions
    • 102105
    • C. Hao, L. Hsiao and H.-L. Li, Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions, J. Math. Phys., 48 (2007), 102105, 11 pp.
    • (2007) J. Math. Phys. , vol.48
    • Hao, C.1    Hsiao, L.2    Li, H.-L.3
  • 13
    • 44649171565 scopus 로고    scopus 로고
    • Bright solitary waves of atomic boseeinstein condensates under rotation
    • N. A. Jamaludin, N. G. Parker and A. M. Martin, Bright solitary waves of atomic BoseEinstein condensates under rotation, Phys. Rev. A, 77 (2008), 051603.
    • (2008) Phys. Rev. A , vol.77 , pp. 051603
    • Jamaludin, N.A.1    Parker, N.G.2    Martin, A.M.3
  • 14
    • 0000387301 scopus 로고
    • Self-similar solutions of the pseudo-conformally invariant nonlinear schrödinger equation
    • O. Kavian and F. Weissler, Self-similar solutions of the pseudo-conformally invariant nonlinear Schrödinger equation, Michigan Math. J., 41 (1994), 151-173.
    • (1994) Michigan Math. J. , vol.41 , pp. 151-173
    • Kavian, O.1    Weissler, F.2
  • 15
    • 0000175040 scopus 로고
    • On a construction of the fundamental solution for schrödinger equations
    • H. Kitada, On a construction of the fundamental solution for Schrödinger equations, J. Fac. Sci. Univ. Tokyo Sec. IA Math., 27 (1980), 193-226.
    • (1980) J. Fac. Sci. Univ. Tokyo Sec. IA Math. , vol.27 , pp. 193-226
    • Kitada, H.1
  • 16
    • 33645993919 scopus 로고    scopus 로고
    • Derivation of the gross-pitaevskii equation for rotating bose gases
    • DOI 10.1007/s00220-006-1524-9
    • E. Lieb and R. Seiringer, Derivation of the Gross-Pitaevskii equation for rotating Bose gases, Comm. Math. Phys., 264 (2006), 505-537. (Pubitemid 43593302)
    • (2006) Communications in Mathematical Physics , vol.264 , Issue.2 , pp. 505-537
    • Lieb, E.H.1    Seiringer, R.2
  • 17
    • 29344463413 scopus 로고    scopus 로고
    • Critical thresholds in the semiclassical limit of 2-d rotational schrödinger equations
    • H. Liu, Critical thresholds in the semiclassical limit of 2-D rotational Schrödinger equations, Z. Angew. Math. Phys., 57 (2006), 42-58.
    • (2006) Z. Angew. Math. Phys. , vol.57 , pp. 42-58
    • Liu, H.1
  • 18
    • 44349088142 scopus 로고    scopus 로고
    • Rigorous derivation of the hydrodynamical equations for rotating superfluids
    • DOI 10.1142/S0218202508002826, PII S0218202508002826
    • H. Liu and C. Sparber, Rigorous derivation of the hydrodynamical equations for rotating superuids, Math. Models Methods Appl. Sci., 18 (2008), 689-706. (Pubitemid 351730145)
    • (2008) Mathematical Models and Methods in Applied Sciences , vol.18 , Issue.5 , pp. 689-706
    • Liu, H.1    Sparber, C.2
  • 19
    • 0347270355 scopus 로고    scopus 로고
    • Rotation prevents finite-time breakdown
    • H. Liu and E. Tadmor, Rotation prevents finite-time breakdown, Phys. D, 188 (2004), 262-276.
    • (2004) Phys. D , vol.188 , pp. 262-276
    • Liu, H.1    Tadmor, E.2
  • 21
    • 0035858573 scopus 로고    scopus 로고
    • Stationary states of a rotating Bose-Einstein condensate: Routes to vortex nucleation
    • DOI 10.1103/PhysRevLett.86.4443
    • K. W. Madison, F. Chevy, V. Bretin and J. Dalibard, Stationary states of a rotating BoseEinstein condensate: Routes to vortex nucleation, Phys. Rev. Lett., 86 (2001), 4443-4446. (Pubitemid 32471359)
    • (2001) Physical Review Letters , vol.86 , Issue.20 , pp. 4443-4446
    • Madison, K.W.1    Chevy, F.2    Bretin, V.3    Dalibard, J.4
  • 23
    • 79961212882 scopus 로고    scopus 로고
    • On the blow up phenomenon for the l2 critical non linear schrödinger equation, in "lectures on nonlinear dispersive equations
    • Gakkōtosho, Tokyo
    • P. Raphaël, On the blow up phenomenon for the L2 critical non linear Schrödinger equation, in "Lectures on Nonlinear Dispersive Equations," GAKUTO Internat. Ser. Math. Sci. Appl., 27, Gakkōtosho, Tokyo, (2006), 9-61.
    • (2006) GAKUTO Internat. Ser. Math. Sci. Appl. , vol.27 , pp. 9-61
    • Raphaël, P.1
  • 24
    • 0036768595 scopus 로고    scopus 로고
    • Gross-Pitaevskii theory of the rotating Bose gas
    • DOI 10.1007/s00220-002-0695-2
    • R. Seiringer, Gross-Pitaevskii theory of the rotating Bose gas, Comm. Math. Phys., 229 (2002), 491-509. (Pubitemid 36185809)
    • (2002) Communications in Mathematical Physics , vol.229 , Issue.3 , pp. 491-509
    • Seiringer, R.1
  • 26
    • 79961087126 scopus 로고    scopus 로고
    • Attractive bose-einstein condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps
    • M. C. Tsatsos, Attractive Bose-Einstein Condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps, Phys. Rev. A, 83 (2011), 063615.
    • (2011) Phys. Rev. A , vol.83 , pp. 063615
    • Tsatsos, M.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.