메뉴 건너뛰기




Volumn 235, Issue 1, 2006, Pages 171-192

On the blow up phenomenon of the critical nonlinear Schrödinger equation

Author keywords

Blow up; Mass concentration; Time dependent Schr dinger equation

Indexed keywords


EID: 33645945606     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.10.005     Document Type: Article
Times cited : (123)

References (21)
  • 1
    • 0033074557 scopus 로고    scopus 로고
    • High frequency approximation of solutions to critical nonlinear wave equations
    • Bahouri H., and Gérard P. High frequency approximation of solutions to critical nonlinear wave equations. Amer. J. Math. 121 (1999) 131-175
    • (1999) Amer. J. Math. , vol.121 , pp. 131-175
    • Bahouri, H.1    Gérard, P.2
  • 2
    • 0000193318 scopus 로고    scopus 로고
    • Refinements of Strichartz inequality and applications to 2D-NLS with critical nonlinearity
    • Bourgain J. Refinements of Strichartz inequality and applications to 2D-NLS with critical nonlinearity. Int. Math. Res. Not. 8 (1998) 253-283
    • (1998) Int. Math. Res. Not. , vol.8 , pp. 253-283
    • Bourgain, J.1
  • 3
    • 33645938991 scopus 로고    scopus 로고
    • 2-critical case, Trans. Amer. Math. Soc., in press
  • 4
    • 10244238584 scopus 로고
    • An Introduction to Nonlinear Schrödinger Equations
    • Univ. Fed. Rio de Janeiro
    • Cazenave T. An Introduction to Nonlinear Schrödinger Equations. Text. Metod. Mat. vol. 26 (1993), Univ. Fed. Rio de Janeiro
    • (1993) Text. Metod. Mat. , vol.26
    • Cazenave, T.1
  • 5
    • 0042904653 scopus 로고    scopus 로고
    • Profile decomposition for the Navier-Stokes equations
    • Gallagher I. Profile decomposition for the Navier-Stokes equations. Bull. Soc. Math. France 129 2 (2001) 285-316
    • (2001) Bull. Soc. Math. France , vol.129 , Issue.2 , pp. 285-316
    • Gallagher, I.1
  • 6
    • 0035217268 scopus 로고    scopus 로고
    • Profile decomposition for the wave equation outside a convex obstacle
    • Gallagher I., and Gérard P. Profile decomposition for the wave equation outside a convex obstacle. J. Math. Pures Appl. (9) 80 1 (2001) 1-49
    • (2001) J. Math. Pures Appl. (9) , vol.80 , Issue.1 , pp. 1-49
    • Gallagher, I.1    Gérard, P.2
  • 7
    • 0000555922 scopus 로고
    • Scattering theory in the energy space for a class of nonlinear Schrödinger equations
    • Ginibre J., and Velo G. Scattering theory in the energy space for a class of nonlinear Schrödinger equations. J. Math. Pures Appl. (9) 64 (1984) 363-401
    • (1984) J. Math. Pures Appl. (9) , vol.64 , pp. 363-401
    • Ginibre, J.1    Velo, G.2
  • 8
    • 0035922239 scopus 로고    scopus 로고
    • On the defect of compactness for the Strichartz estimates of the Schrödinger equations
    • Keraani S. On the defect of compactness for the Strichartz estimates of the Schrödinger equations. J. Differential Equations 175 2 (2001) 353-392
    • (2001) J. Differential Equations , vol.175 , Issue.2 , pp. 353-392
    • Keraani, S.1
  • 9
    • 0001337201 scopus 로고
    • Construction of solutions with exactly k blow up points for nonlinear Schrödinger equations with critical nonlinearity
    • Merle F. Construction of solutions with exactly k blow up points for nonlinear Schrödinger equations with critical nonlinearity. Comm. Math. Phys. 129 2 (1990) 223-240
    • (1990) Comm. Math. Phys. , vol.129 , Issue.2 , pp. 223-240
    • Merle, F.1
  • 10
    • 84974001368 scopus 로고
    • Determination of blow up solutions with minimal mass for nonlinear Schrödinger equations with critical power
    • Merle F. Determination of blow up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Duke Math. J. 69 2 (1993) 427-454
    • (1993) Duke Math. J. , vol.69 , Issue.2 , pp. 427-454
    • Merle, F.1
  • 11
    • 2942586742 scopus 로고    scopus 로고
    • 2 critical nonlinear Schrödinger equation
    • 2 critical nonlinear Schrödinger equation. Invent. Math. 156 3 (2004) 565-672
    • (2004) Invent. Math. , vol.156 , Issue.3 , pp. 565-672
    • Merle, F.1    Raphael, R.P.2
  • 12
    • 0000704928 scopus 로고
    • 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
    • 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. J. Differential Equations 84 2 (1990) 205-214
    • (1990) J. Differential Equations , vol.84 , Issue.2 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 13
    • 1842709141 scopus 로고    scopus 로고
    • 2 solutions of the critical nonlinear Schrödinger equations in 2D
    • 2 solutions of the critical nonlinear Schrödinger equations in 2D. Int. Math. Res. Not. 8 (1998) 399-425
    • (1998) Int. Math. Res. Not. , vol.8 , pp. 399-425
    • Merle, F.1    Vega, L.2
  • 15
    • 0033484486 scopus 로고    scopus 로고
    • Asymptotic and limiting profiles of blow up solutions of the nonlinear Schrödinger equation with critical power
    • Nawa H. Asymptotic and limiting profiles of blow up solutions of the nonlinear Schrödinger equation with critical power. Comm. Pure Appl. Math. 52 2 (1999) 193-270
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.2 , pp. 193-270
    • Nawa, H.1
  • 16
    • 0003230098 scopus 로고    scopus 로고
    • The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse
    • Springer-Verlag, New York
    • Sulem C. The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse. Appl. Math. Sci. vol. 139 (1999), Springer-Verlag, New York
    • (1999) Appl. Math. Sci. , vol.139
    • Sulem, C.1
  • 17
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equation
    • Strichartz R. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equation. Duke Math. J. 44 (1977) 705-714
    • (1977) Duke Math. J. , vol.44 , pp. 705-714
    • Strichartz, R.1
  • 18
    • 84968496791 scopus 로고
    • A restriction theorem for the Fourier transform
    • Tomas P. A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc. 81 (1975) 477-478
    • (1975) Bull. Amer. Math. Soc. , vol.81 , pp. 477-478
    • Tomas, P.1
  • 19
    • 0040580243 scopus 로고
    • 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power
    • 2 concentration of blow up solutions for the nonlinear Schrödinger equation with critical power. Nonlinear Anal. 15 8 (1990) 719-724
    • (1990) Nonlinear Anal. , vol.15 , Issue.8 , pp. 719-724
    • Tsutsumi, Y.1
  • 20
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • Weinstein M.I. Nonlinear Schrödinger equations and sharp interpolation estimates. Comm. Math. Phys. 87 (1983) 567-576
    • (1983) Comm. Math. Phys. , vol.87 , pp. 567-576
    • Weinstein, M.I.1
  • 21
    • 0001295566 scopus 로고
    • On the structure of singularities in solutions to the nonlinear dispersive evolution equations
    • Weinstein M.I. On the structure of singularities in solutions to the nonlinear dispersive evolution equations. Comm. Partial Differential Equations 11 (1984) 545-565
    • (1984) Comm. Partial Differential Equations , vol.11 , pp. 545-565
    • Weinstein, M.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.