메뉴 건너뛰기




Volumn 282, Issue 2, 2008, Pages 435-467

A sharp condition for scattering of the radial 3D cubic nonlinear schrödinger equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 47749109045     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0529-y     Document Type: Article
Times cited : (301)

References (34)
  • 1
    • 0034250857 scopus 로고    scopus 로고
    • Stability criterion for attractive Bose-Einstein condensates
    • 2
    • Bergé L., Alexander T., Kivshar Y.: Stability criterion for attractive Bose-Einstein condensates. Phys. Rev. A 62(2), 023607 (2000)
    • (2000) Phys. Rev. A , vol.62 , pp. 023607
    • Bergé, L.1    Alexander, T.2    Kivshar, Y.3
  • 2
    • 33646364123 scopus 로고    scopus 로고
    • Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation
    • 2
    • Bégout P.: Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation. Adv. Math. Sci. Appl. 12(2), 817-827 (2002)
    • (2002) Adv. Math. Sci. Appl. , vol.12 , pp. 817-827
    • Bégout, P.1
  • 3
    • 5444256656 scopus 로고    scopus 로고
    • Semilinear Schrödinger equations
    • New York: New York University, Courant Institute of Mathematical Sciences, Providence, RI: Amer. Math. Soc.
    • Cazenave, T.: Semilinear Schrödinger equations. Courant Lecture Notes in Mathematics, 10. New York: New York University, Courant Institute of Mathematical Sciences, Providence, RI: Amer. Math. Soc. 2003
    • (2003) Courant Lecture Notes in Mathematics , vol.10
    • Cazenave, T.1
  • 8
    • 41549106651 scopus 로고    scopus 로고
    • Some modern aspects of self-focusing theory
    • R.W. Boyd, S.G. Lukishova, Y.R. Shen, eds., to be published by Springer, in August 2008, available at
    • Fibich, G.: Some modern aspects of self-focusing theory. In: Self-Focusing: Past and Present, R.W. Boyd, S.G. Lukishova, Y.R. Shen, eds., to be published by Springer, in August 2008, available at http://www.math.tau.ac. il/%7Efibich/Manuscripts/Fibich_G_SF_Springer.pdf
    • Self-focusing: Past and Present
    • Fibich, G.1
  • 9
    • 85189364433 scopus 로고    scopus 로고
    • Inhomogeneous Strichartz estimates
    • 1
    • Foschi D.: Inhomogeneous Strichartz estimates. J. Hyper. Diff. Eq. 2(1), 1-24 (2005)
    • (2005) J. Hyper. Diff. Eq. , vol.2 , pp. 1-24
    • Foschi, D.1
  • 10
    • 49249140378 scopus 로고
    • On a class of nonlinear Schrödinger equation. I. the Cauchy problems; II. Scattering theory, general case
    • 1-32
    • Ginibre J., Velo G.: On a class of nonlinear Schrödinger equation. I. The Cauchy problems; II. Scattering theory, general case. J. Funct. Anal. 32(1-32), 33-71 (1979)
    • (1979) J. Funct. Anal. , vol.32 , pp. 33-71
    • Ginibre, J.1    Velo, G.2
  • 11
    • 0000555922 scopus 로고
    • Scattering theory in the energy space for a class of nonlinear Schrödinger equations
    • 4
    • Ginibre J., Velo G.: Scattering theory in the energy space for a class of nonlinear Schrödinger equations. J. Math. Pures Appl. (9) 64(4), 363-401 (1985)
    • (1985) J. Math. Pures Appl. (9) , vol.64 , pp. 363-401
    • Ginibre, J.1    Velo, G.2
  • 12
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equation
    • 9
    • Glassey R.T.: On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equation. J. Math. Phys. 18(9), 1794-1797 (1977)
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassey, R.T.1
  • 13
    • 77955700830 scopus 로고    scopus 로고
    • On blow-up solutions to the 3D cubic nonlinear Schrödinger equation.
    • article ID abm004, doi: 10.1093/amrx/abm004
    • Holmer, J., Roudenko, S.: On blow-up solutions to the 3D cubic nonlinear Schrödinger equation. Appl. Math. Res. Express, Vol. 2007, article ID abm004, doi: 10.1093/amrx/abm004, 2007
    • (2007) Appl. Math. Res. Express
    • Holmer, J.1    Roudenko, S.2
  • 14
    • 0041172171 scopus 로고
    • q,r -theory for nonlinear Schrödinger equations
    • In: Spectral and scattering theory and applications, Tokyo: Math. Soc. Japan
    • q,r -theory for nonlinear Schrödinger equations. In: Spectral and scattering theory and applications, Adv. Stud. Pure Math., 23, Tokyo: Math. Soc. Japan, 1994, pp. 223-238
    • (1994) Adv. Stud. Pure Math. , vol.23 , pp. 223-238
    • Kato, T.1
  • 15
    • 0035922239 scopus 로고    scopus 로고
    • On the defect of compactness for the Strichartz estimates of the Schrödinger equation
    • Keraani S.: On the defect of compactness for the Strichartz estimates of the Schrödinger equation. J. Diff. Eq. 175, 353-392 (2001)
    • (2001) J. Diff. Eq. , vol.175 , pp. 353-392
    • Keraani, S.1
  • 16
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • Keel M., Tao T.: Endpoint Strichartz estimates. Amer. J. Math. 120, 955-980 (1998)
    • (1998) Amer. J. Math. , vol.120 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 17
    • 33750526878 scopus 로고    scopus 로고
    • Global well-posedness, scattering, and blow-up for the energy-critical focusing nonlinear Schrödinger equation in the radial case
    • 3
    • Kenig C.E., Merle F.: Global well-posedness, scattering, and blow-up for the energy-critical focusing nonlinear Schrödinger equation in the radial case. Invent. Math. 166(3), 645-675 (2006)
    • (2006) Invent. Math. , vol.166 , pp. 645-675
    • Kenig, C.E.1    Merle, F.2
  • 18
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • 4
    • Kenig C., Ponce G., Vega L.: Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Comm. Pure Appl. Math. 46(4), 527-620 (1993)
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 19
    • 44949272407 scopus 로고
    • Computer simulation of wave collapses in the nonlinear Schrödinger equation
    • Kosmatova N.E., Shvets V.F., Zakharov V.E.: Computer simulation of wave collapses in the nonlinear Schrödinger equation. Physica D 52, 16-35 (1991)
    • (1991) Physica D , vol.52 , pp. 16-35
    • Kosmatova, N.E.1    Shvets, V.F.2    Zakharov, V.E.3
  • 23
    • 0000835523 scopus 로고
    • 1 solution for the Nonlinear Schrödinger Equation
    • 1 solution for the Nonlinear Schrödinger Equation. J. Diff. Eq. 92, 317-330 (1991)
    • (1991) J. Diff. Eq. , vol.92 , pp. 317-330
    • Ogawa, T.1    Tsutsumi, Y.2
  • 24
    • 33749001728 scopus 로고    scopus 로고
    • Derivation of the Gross-Pitaevskii hierarchy.
    • In: Mathematical physics of quantum mechanics. , Berlin: Springer, see also arxiv.org, 2005
    • Schlein, B.: Derivation of the Gross-Pitaevskii hierarchy. In: Mathematical physics of quantum mechanics, Lecture Notes in Phys., 690, Berlin: Springer, 2006, pp. 279-293, see also arxiv.org http://arXiv.org/list/math-ph/ 0504078, 2005
    • (2006) Lecture Notes in Phys. , vol.690 , pp. 279-293
    • Schlein, B.1
  • 25
    • 47749149259 scopus 로고    scopus 로고
    • Soliton dynamics and scattering
    • (Madrid, Spain, 2006), Zurich: European Math. Soc.
    • Soffer, A.: Soliton dynamics and scattering. In: Proceedings of the International Congress of Mathematicians, (Madrid, Spain, 2006), Zurich: European Math. Soc., 2006, pp. 459-471
    • (2006) Proceedings of the International Congress of Mathematicians , pp. 459-471
    • Soffer, A.1
  • 26
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher dimensions
    • 2
    • Strauss W.A.: Existence of solitary waves in higher dimensions. Commun. Math. Phys. 55(2), 149-162 (1977)
    • (1977) Commun. Math. Phys. , vol.55 , pp. 149-162
    • Strauss, W.A.1
  • 27
    • 0003230098 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation. Self-focusing and wave collapse
    • New York: Springer-Verlag
    • Sulem, C., Sulem, P-L.: The nonlinear Schrödinger equation. Self-focusing and wave collapse. Applied Mathematical Sciences, 139. New York: Springer-Verlag, 1999
    • (1999) Applied Mathematical Sciences , vol.139
    • Sulem, C.1    Sulem, P.-L.2
  • 28
    • 15944416090 scopus 로고    scopus 로고
    • On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation
    • 1
    • Tao T.: On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation. Dyn. Partial Differ. Equ. 1(1), 1-48 (2004)
    • (2004) Dyn. Partial Differ. Equ. , vol.1 , pp. 1-48
    • Tao, T.1
  • 29
    • 44849106120 scopus 로고    scopus 로고
    • A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations
    • Tao T.: A (concentration-)compact attractor for high-dimensional non-linear Schrödinger equations. Dynamics of PDE 4, 1-53 (2007)
    • (2007) Dynamics of PDE , vol.4 , pp. 1-53
    • Tao, T.1
  • 30
    • 34249655802 scopus 로고    scopus 로고
    • Nonlinear dispersive equations. Local and global analysis
    • Published for the Conference Board of the Mathematical Sciences, Washington, DC, Providence, RI: Amer. Math. Soc
    • Tao, T.: 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, Providence, RI: Amer. Math. Soc. 2006
    • (2006) CBMS Regional Conference Series in Mathematics , vol.106
    • Tao, T.1
  • 31
    • 0035379526 scopus 로고    scopus 로고
    • Regularity of solutions to the free Schrödinger equation with radial initial data
    • 2
    • Vilela M.: Regularity of solutions to the free Schrödinger equation with radial initial data. Illinois J. Math. 45(2), 361-370 (2001)
    • (2001) Illinois J. Math. , vol.45 , pp. 361-370
    • Vilela, M.1
  • 32
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • 4
    • Weinstein M.: Nonlinear Schrödinger equations and sharp interpolation estimates. Commun. Math. Phys. 87(4), 567-576 (1982)
    • (1982) Commun. Math. Phys. , vol.87 , pp. 567-576
    • Weinstein, M.1
  • 33
    • 0000899292 scopus 로고
    • Collapse of Langmuir waves
    • in Russian
    • Zakharov, V.E.: Collapse of Langmuir waves, Zh. Eksp. Teor. Fiz. 62, 1745-1751 (1972), (in Russian);
    • (1972) Zh. Eksp. Teor. Fiz , vol.62 , pp. 1745-1751
    • Zakharov, V.E.1
  • 34
    • 0001596227 scopus 로고
    • English
    • Sov. Phys. JETP, 35 908-914 (1972), (English)
    • (1972) Sov. Phys. JETP , vol.35 , pp. 908-914


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.