메뉴 건너뛰기




Volumn 9, Issue 1, 2003, Pages 31-54

Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm

Author keywords

Orbital stability; Schr dinger equation; Upper bound on sobolev norms

Indexed keywords


EID: 0037254091     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2003.9.31     Document Type: Article
Times cited : (28)

References (27)
  • 1
    • 23244446904 scopus 로고
    • Critical nonlinear Schrödinger Equation
    • T. Cazenave, F.B. Weissler, Critical nonlinear Schrödinger Equation, Non. Anal. TMA, 14 (1990), 807-836.
    • (1990) Non. Anal. TMA , vol.14 , pp. 807-836
    • Cazenave, T.1    Weissler, F.B.2
  • 2
    • 34250084341 scopus 로고
    • Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
    • J. Bourgain, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Part I, Geometric and Funct. Anal. 3 (1993), 107-156.
    • (1993) Part I, Geometric and Funct. Anal. , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 3
    • 1842450240 scopus 로고    scopus 로고
    • On the growth in time of higher order Sobolev norms of smooth solutions of Hamiltonian PDE
    • J. Bourgain, On the growth in time of higher order Sobolev norms of smooth solutions of Hamiltonian PDE, IMRN 6 (1996), 277-304.
    • (1996) IMRN , vol.6 , pp. 277-304
    • Bourgain, J.1
  • 4
    • 0000193318 scopus 로고    scopus 로고
    • Refinements of strichartz inequality and applications to 2d-NLS with critical nonlinearity
    • J. Bourgain, Refinements of Strichartz Inequality and Applications to 2d-NLS With Critical Nonlinearity, Inter. Math. Res. Not., (1998), p. 253-284.
    • (1998) Inter. Math. Res. Not. , pp. 253-284
    • Bourgain, J.1
  • 5
    • 0000046869 scopus 로고    scopus 로고
    • Scattering in the energy space and below for 3D NLS
    • J. Bourgain, Scattering in the energy space and below for 3D NLS, J. Anal. Math. 75 (1998), 267-297.
    • (1998) J. Anal. Math. , vol.75 , pp. 267-297
    • Bourgain, J.1
  • 7
    • 0015249887 scopus 로고
    • 3 = 0 and a variational characterization of other solutions
    • 3 = 0 and a variational characterization of other solutions, Arch. Rat. Mech. Anal. 46 (1972), 81-95.
    • (1972) Arch. Rat. Mech. Anal. , vol.46 , pp. 81-95
    • Coffman, C.V.1
  • 12
    • 0012952192 scopus 로고    scopus 로고
    • Global well-posedness result for KdV in Sobolev spaces of negative index
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness result for KdV in Sobolev spaces of negative index, EJDE 2001 (2001) No 26, 1-7.
    • (2001) EJDE , vol.2001 , Issue.26 , pp. 1-7
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 14
    • 0012910981 scopus 로고    scopus 로고
    • A refined global well-posedness result for the Schrödinger equations with derivative
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, A refined global well-posedness result for the Schrödinger equations with derivative, to appear, Siam J. Math.
    • Siam J. Math.
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 17
    • 33747492074 scopus 로고    scopus 로고
    • Le probléme de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace, Séminaire Bourbaki 1994/1995
    • Exp. 796
    • J. Ginibre, Le probléme de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace, Séminaire Bourbaki 1994/1995, Astérisque 237 (1996), Exp. 796, 163-187.
    • (1996) Astérisque , vol.237 , pp. 163-187
    • Ginibre, J.1
  • 18
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint strichartz estimates
    • M. Keel, T. Tao, Endpoint Strichartz Estimates, Amer. Math. J. 120 (1998), 955-980.
    • (1998) Amer. Math. J. , vol.120 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 19
    • 0001646511 scopus 로고    scopus 로고
    • 1+1 for rough data
    • 1+1 for rough data, IMRN 21 (1998), 1117-1156.
    • (1998) IMRN , vol.21 , pp. 1117-1156
    • Keel, M.1    Tao, T.2
  • 21
    • 0001442617 scopus 로고    scopus 로고
    • On the ill-posedness of some canonical dispersive equations
    • C. Kenig, G. Ponce, L. Vega, On the ill-posedness of some canonical dispersive equations, Duke Math. J. 3 (2001), 617-633.
    • (2001) Duke Math. J. , vol.3 , pp. 617-633
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 22
    • 0012910983 scopus 로고    scopus 로고
    • Stability of the blowup profile and lower bounds for blowup rate for the critical generalized KdV equation
    • Y. Martel, F. Merle, Stability of the blowup profile and lower bounds for blowup rate for the critical generalized KdV equation, to appear, Annals of Math.
    • Annals of Math
    • Martel, Y.1    Merle, F.2
  • 23
    • 0001304838 scopus 로고    scopus 로고
    • Energy scattering for non-linear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2
    • K. Nakanishi, Energy scattering for non-linear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2, JFA 169 (1999), 201-225.
    • (1999) JFA , vol.169 , pp. 201-225
    • Nakanishi, K.1
  • 24
    • 0041157182 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), 109-142.
    • (1997) Duke Math J. , vol.86 , pp. 109-142
    • Staffilani, G.1
  • 25
    • 0000237067 scopus 로고
    • 2 solutions for nonlinear Schrödinger equations and nonlinear groups
    • 2 solutions for nonlinear Schrödinger equations and nonlinear groups, Funk. Ekva. 30 (1987), 115-125.
    • (1987) Funk. Ekva. , vol.30 , pp. 115-125
    • Tsutsumi, Y.1
  • 26
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • M. Weinstein, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16 (1985), 472-491.
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 472-491
    • Weinstein, M.1
  • 27
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive equations
    • M. Weinstein, Lyapunov stability of ground states of nonlinear dispersive equations, CPAM 39 (1986), 51-68.
    • (1986) CPAM , vol.39 , pp. 51-68
    • Weinstein, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.