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Volumn 21, Issue 3, 2008, Pages 665-686

Resonant decompositions and the I-method for the cubic nonlinear schrodinger equation on ℝ2

Author keywords

Nonlinear Schr dinger equation; Resonant decomposition; Strichartz estimates; Well posedness

Indexed keywords


EID: 45849140568     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (80)

References (36)
  • 1
    • 34948812627 scopus 로고    scopus 로고
    • Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds
    • D. Bambusi, J.-M. Delort, B. Grebert and J. Szeftel, Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds, Comm. Pure Appl. Math., 60 (2007), 1665-1690.
    • (2007) Comm. Pure Appl. Math , vol.60 , pp. 1665-1690
    • Bambusi, D.1    Delort, J.-M.2    Grebert, B.3    Szeftel, J.4
  • 3
    • 0030158684 scopus 로고    scopus 로고
    • On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations
    • B. Birnir, C. Kenig, G. Ponce, N. Svanstedt and L. Vega, On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations, J. London Math. Soc. 53 (1996), 551-559.
    • (1996) J. London Math. Soc , vol.53 , pp. 551-559
    • Birnir, B.1    Kenig, C.2    Ponce, G.3    Svanstedt, N.4    Vega, L.5
  • 5
    • 0000193318 scopus 로고    scopus 로고
    • Refinement of Strichartz inequality and applications to 2D-NLS with critical nonlinearity
    • J. Bourgain, Refinement of Strichartz inequality and applications to 2D-NLS with critical nonlinearity, Internat. Math. Res. Notices, 5 (1998), 253-283.
    • (1998) Internat. Math. Res. Notices , vol.5 , pp. 253-283
    • Bourgain, J.1
  • 7
    • 14644430957 scopus 로고    scopus 로고
    • A remark on normal forms and the "I-method" for periodic NLS
    • J. Bourgain, A remark on normal forms and the "I-method" for periodic NLS, J. Anal. Math., 94 (2004), 125-157.
    • (2004) J. Anal. Math , vol.94 , pp. 125-157
    • Bourgain, J.1
  • 8
    • 1842450240 scopus 로고    scopus 로고
    • On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE
    • J. Bourgain, On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE, Internat. Math. Res. Notices, 1996, 277-304.
    • (1996) Internat. Math. Res. Notices , pp. 277-304
    • Bourgain, J.1
  • 9
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger Equations
    • New York University, Courant Institute of Mathematical Sciences, AMS
    • T. Cazenave, "Semilinear Schrödinger Equations," Courant Lecture Notes in Mathematics, 10, New York University, Courant Institute of Mathematical Sciences, AMS, 2003.
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 11
    • 23244446904 scopus 로고
    • The Cauchy problem for the critical nonlinear Schrödinger equation
    • T. Cazenave and P. B. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation, Non. Anal. TMA, 14 (1990), 807-836.
    • (1990) Non. Anal. TMA , vol.14 , pp. 807-836
    • Cazenave, T.1    Weissler, P.B.2
  • 12
    • 45849100799 scopus 로고    scopus 로고
    • M. Christ, J. Colliander and T. Tao, Ill-posedness for nonlinear Schrödinger and wave equations, preprint, 2003. arxiv: 0311048
    • M. Christ, J. Colliander and T. Tao, Ill-posedness for nonlinear Schrödinger and wave equations, preprint, 2003. arxiv: 0311048
  • 14
    • 68049128568 scopus 로고    scopus 로고
    • 2, Int. Math. Res. Not. IMRN, 2007, Art. ID rnm090.
    • 2, Int. Math. Res. Not. IMRN, 2007, Art. ID rnm090.
  • 17
    • 0037254091 scopus 로고    scopus 로고
    • Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm. Discrete Contin. Dyn. Syst., 9 (2003), 31-54.
    • (2003) Discrete Contin. Dyn. Syst , vol.9 , pp. 31-54
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 18
    • 23244434956 scopus 로고    scopus 로고
    • Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm, Commun. Pure Appl. Anal., 2 (2003), 33-50.
    • (2003) Commun. Pure Appl. Anal , vol.2 , pp. 33-50
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 19
    • 0037287349 scopus 로고    scopus 로고
    • A refined global well-posedness result for Schrödinger equations with derivative
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, A refined global well-posedness result for Schrödinger equations with derivative, SIAM J. Math. Anal., 34 (2002), 64-86.
    • (2002) SIAM J. Math. Anal , vol.34 , pp. 64-86
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 20
    • 0036771238 scopus 로고    scopus 로고
    • Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, Math. Res. Letters, 9 (2002), 1-24.
    • (2002) Math. Res. Letters , vol.9 , pp. 1-24
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 22
    • 45849132309 scopus 로고    scopus 로고
    • 3, to appear, Annals Math., arxiv:0402129
    • 3, to appear, Annals Math., arxiv:0402129
  • 24
    • 0001123370 scopus 로고
    • Smoothing properties and retarded estimates for some dispersive evolution equations
    • J. Ginibre and G. Velo, Smoothing properties and retarded estimates for some dispersive evolution equations, Comm. Math. Phys., 144 (1992), 163-188.
    • (1992) Comm. Math. Phys , vol.144 , pp. 163-188
    • Ginibre, J.1    Velo, G.2
  • 26
    • 51649139542 scopus 로고
    • s-solutions and unconditional well-posedness
    • s-solutions and unconditional well-posedness, J. Anal. Math., 67 (1995), 281-306.
    • (1995) J. Anal. Math , vol.67 , pp. 281-306
    • Kato, T.1
  • 29
    • 33645945606 scopus 로고    scopus 로고
    • On the blow-up phenomenon of the critical nonlinear Schrödinger equation
    • S. Keraani, On the blow-up phenomenon of the critical nonlinear Schrödinger equation, J. Funct. Anal., 235 (2006), 171-192.
    • (2006) J. Funct. Anal , vol.235 , pp. 171-192
    • Keraani, S.1
  • 30
    • 0036350601 scopus 로고    scopus 로고
    • Dispersive estimates and the 2D cubic NLS equation
    • F. Planchon, Dispersive estimates and the 2D cubic NLS equation, J. Anal. Math., 86 (2002), 319-334.
    • (2002) J. Anal. Math , vol.86 , pp. 319-334
    • Planchon, F.1
  • 31
    • 0002487390 scopus 로고    scopus 로고
    • On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations
    • G. Staffilani, On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations, Duke Math J., 86 (1997), 79-107.
    • (1997) Duke Math J , vol.86 , pp. 79-107
    • Staffilani, G.1
  • 32
    • 45849126425 scopus 로고    scopus 로고
    • T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS Regional Conference Series in Mathematics, 106. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006.
    • T. Tao, "Nonlinear Dispersive Equations: Local and Global Analysis," CBMS Regional Conference Series in Mathematics, 106. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006.
  • 33
    • 45849144298 scopus 로고    scopus 로고
    • T. Tao, A pseudoconformal compactification of the nonlinear Schrödinger equation and applications, preprint, 2006. arxiv:0606254
    • T. Tao, A pseudoconformal compactification of the nonlinear Schrödinger equation and applications, preprint, 2006. arxiv:0606254
  • 34
    • 45849134794 scopus 로고    scopus 로고
    • T. Tao, M. Visan and X. Zhang, Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in higher dimensions, preprint, 2006. arxiv:0609692
    • T. Tao, M. Visan and X. Zhang, Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in higher dimensions, preprint, 2006. arxiv:0609692
  • 35
    • 0001270511 scopus 로고
    • Scattering problem, for nonlinear Schrödinger equations
    • Y. Tsutsumi, Scattering problem, for nonlinear Schrödinger equations, Ann. Inst. H. Poincare, Phys. Theor., 43 (1985), 321-347.
    • (1985) Ann. Inst. H. Poincare, Phys. Theor , vol.43 , pp. 321-347
    • Tsutsumi, Y.1
  • 36
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M. I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys., 87 (1983), 567-576.
    • (1983) Commun. Math. Phys , vol.87 , pp. 567-576
    • Weinstein, M.I.1


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