메뉴 건너뛰기




Volumn 20, Issue 5, 2008, Pages 881-919

Minimal-mass blowup solutions of the mass-critical NLS

Author keywords

[No Author keywords available]

Indexed keywords


EID: 55549086472     PISSN: 09337741     EISSN: 14355337     Source Type: Journal    
DOI: 10.1515/FORUM.2008.042     Document Type: Article
Times cited : (122)

References (44)
  • 1
    • 0033074557 scopus 로고    scopus 로고
    • High frequency approximation of solutions to critical nonlinear wave equations
    • Bahouri H., 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
    • 55549107108 scopus 로고    scopus 로고
    • 2-critical nonlinear Schrödinger equation
    • preprint
    • 2-critical nonlinear Schrödinger equation, preprint
    • Begout, P.1    Vargas, A.2
  • 3
    • 55549112514 scopus 로고    scopus 로고
    • 2-critical NLS
    • preprint math.AP/0508001
    • 2-critical NLS, preprint math.AP/0508001
    • Blue, P.1    Colliander, J.2
  • 4
    • 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. Inter. Math. Res. Not. 5 (1998), 253-284
    • (1998) Inter. Math. Res. Not , vol.5 , pp. 253-284
    • Bourgain, J.1
  • 5
    • 0040248890 scopus 로고    scopus 로고
    • Global well-posedness of defocusing 3D critical NLS in the radial case
    • Bourgain J.: Global well-posedness of defocusing 3D critical NLS in the radial case. J. Amer. Math. Soc. 12 (1999), 145-171
    • (1999) J. Amer. Math. Soc , vol.12 , pp. 145-171
    • Bourgain, J.1
  • 6
    • 55549135291 scopus 로고    scopus 로고
    • 2-critical case, preprint math.AP/0404201
    • 2-critical case, preprint math.AP/0404201
  • 7
    • 55549131464 scopus 로고    scopus 로고
    • Cazenave T.: Semilinear Schrödinger equations. Courant Lecture Notes in Mathematics 10. New York University, Courant Institute of Mathematical Sciences, AMS, 2003
    • Cazenave T.: Semilinear Schrödinger equations. Courant Lecture Notes in Mathematics 10. New York University, Courant Institute of Mathematical Sciences, AMS, 2003
  • 8
    • 23244446904 scopus 로고
    • Critical nonlinear Schrödinger Equation.
    • Cazenave T., Weissler F. B.: Critical nonlinear Schrödinger Equation. Nonlin. Anal. TMA 14 (1990), 807-836
    • (1990) Nonlin. Anal. TMA , vol.14 , pp. 807-836
    • Cazenave, T.1    Weissler, F.B.2
  • 9
    • 0036771238 scopus 로고    scopus 로고
    • Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation
    • Colliander J., Keel M., Staffilani G., Takaoka H., Tao T.: Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Math Res. Lett. 9 (2002), 659-682
    • (2002) Math Res. Lett , vol.9 , pp. 659-682
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 12
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger problems I. The Cauchy problem, general case
    • Ginibre J., Velo G.: On a class of nonlinear Schrödinger problems I. The Cauchy problem, general case. J. Funct. Anal. 32 (1979), 1-32
    • (1979) J. Funct. Anal , vol.32 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 13
    • 28444450137 scopus 로고    scopus 로고
    • Blowup theory for the critical nonlinear Schrödinger equation revisited
    • Hmidi T., Keraani S.: Blowup theory for the critical nonlinear Schrödinger equation revisited. Int. Math. Res. Not. 46 (2005), 2815-2828
    • (2005) Int. Math. Res. Not , vol.46 , pp. 2815-2828
    • Hmidi, T.1    Keraani, S.2
  • 14
    • 39449124672 scopus 로고    scopus 로고
    • 2-critical nonlinear Schrödinger equations
    • preprint
    • 2-critical nonlinear Schrödinger equations, preprint
    • Hmidi, T.1    Keraani, S.2
  • 15
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz Estimates
    • Keel M., Tao T.: 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
  • 16
    • 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 (2001), 353-392
    • (2001) J. Differential Equations , vol.175 , pp. 353-392
    • Keraani, S.1
  • 17
    • 33645945606 scopus 로고    scopus 로고
    • On the blow-up phenomenon of the critical nonlinear Schrödinger equation
    • Keraani S.: 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
  • 19
    • 0034164847 scopus 로고    scopus 로고
    • A Liouville theorem for the critical generalized Korteweg-de Vries equation
    • Martel Y., Merle F.: A Liouville theorem for the critical generalized Korteweg-de Vries equation. J. Math. Pures Appl. 79 (2000), 339-425
    • (2000) J. Math. Pures Appl , vol.79 , pp. 339-425
    • Martel, Y.1    Merle, F.2
  • 20
    • 33744803549 scopus 로고
    • Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical non-linearity
    • Merle F.: Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical non-linearity. Comm. Math. Phys. 149 (1992), 205-214
    • (1992) Comm. Math. Phys , vol.149 , pp. 205-214
    • Merle, F.1
  • 21
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power
    • Merle F.: Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power. Duke Math. J. 69 (1993), 427-453
    • (1993) Duke Math. J , vol.69 , pp. 427-453
    • Merle, F.1
  • 22
    • 0030353240 scopus 로고    scopus 로고
    • 2 minimal blowup solutions of critical nonlinear Schrödinger equation
    • 2 minimal blowup solutions of critical nonlinear Schrödinger equation. Ann. Inst. Henri Poincare 13 (1996), 553-565
    • (1996) Ann. Inst. Henri Poincare , vol.13 , pp. 553-565
    • Merle, F.1
  • 23
    • 20444437961 scopus 로고    scopus 로고
    • The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrvdinger equation
    • Merle F., Raphael P.: The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrvdinger equation. Ann. of Math. 161 (2005), 157-222
    • (2005) Ann. of Math , vol.161 , pp. 157-222
    • Merle, F.1    Raphael, P.2
  • 24
    • 0041350485 scopus 로고    scopus 로고
    • Sharp upper bound on the blowup rate for the critical nonlinear Schrödinger equation
    • Merle F., Raphael P.: Sharp upper bound on the blowup rate for the critical nonlinear Schrödinger equation. Geom. Funct. Anal. 13 (2003), 591-642
    • (2003) Geom. Funct. Anal , vol.13 , pp. 591-642
    • Merle, F.1    Raphael, P.2
  • 25
    • 2942586742 scopus 로고    scopus 로고
    • 2 critical nonlinear Schrödinger equation
    • 2 critical nonlinear Schrödinger equation. Invent. Math. 156 (2004), 565-672
    • (2004) Invent. Math , vol.156 , pp. 565-672
    • Merle, F.1    Raphael, P.2
  • 26
    • 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. Diff. Equations 84 (1990), 205-214
    • (1990) J. Diff. Equations , vol.84 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 27
    • 1842709141 scopus 로고    scopus 로고
    • 2 solutions of the critical nonlinear Schrödinger equation in 2D
    • 2 solutions of the critical nonlinear Schrödinger equation in 2D. Internat. Math. Res. Not. 8 (1998), 399-425
    • (1998) Internat. Math. Res. Not , vol.8 , pp. 399-425
    • Merle, F.1    Vega, L.2
  • 29
    • 5644242960 scopus 로고    scopus 로고
    • An abstract version of the concentration compactness principle
    • Schinder I., Tintarev K.: An abstract version of the concentration compactness principle. Revista Mathemática Complutense 15 (2002), 417-436
    • (2002) Revista Mathemática Complutense , vol.15 , pp. 417-436
    • Schinder, I.1    Tintarev, K.2
  • 30
    • 84972553620 scopus 로고
    • Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations
    • Strichartz R. S.: Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations. Duke Math. J. 44 (1977), 705-774
    • (1977) Duke Math. J , vol.44 , pp. 705-774
    • Strichartz, R.S.1
  • 31
    • 1142264310 scopus 로고    scopus 로고
    • A sharp bilinear restriction estimate for paraboloids
    • Tao T.: A sharp bilinear restriction estimate for paraboloids. Geom. Func. Anal. 13 (2003), 1359-1384
    • (2003) Geom. Func. Anal , vol.13 , pp. 1359-1384
    • Tao, T.1
  • 32
    • 15944416090 scopus 로고    scopus 로고
    • On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation
    • Tao T.: On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation. Dynamics of PDE 1 (2004), 1-48
    • (2004) Dynamics of PDE , vol.1 , pp. 1-48
    • Tao, T.1
  • 33
    • 15944382285 scopus 로고    scopus 로고
    • Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrödinger equation for radial data
    • Tao T.: Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrödinger equation for radial data. New York J. Math. 11 (2005), 57-80
    • (2005) New York J. Math , vol.11 , pp. 57-80
    • Tao, T.1
  • 34
    • 55549085493 scopus 로고    scopus 로고
    • A pseudoconformal compactification of the nonlinear Schrödinger equation and applications
    • preprint math.AP/0606254
    • Tao T.: A pseudoconformal compactification of the nonlinear Schrödinger equation and applications, preprint math.AP/0606254
    • Tao, T.1
  • 35
    • 55549105374 scopus 로고    scopus 로고
    • Two remarks on the generalised Korteweg-de Vries equation
    • preprint math.AP/0606236
    • Tao T.: Two remarks on the generalised Korteweg-de Vries equation, preprint math.AP/0606236
    • Tao, T.1
  • 36
    • 27644461939 scopus 로고    scopus 로고
    • Tao T., Visan M.: Stability of energy-critical nonlinear Schrödinger equations in high dimensions. Electron. J. Diff. Equations 2005 (2005), No. 118, 1-28
    • Tao T., Visan M.: Stability of energy-critical nonlinear Schrödinger equations in high dimensions. Electron. J. Diff. Equations 2005 (2005), No. 118, 1-28
  • 37
    • 35349015085 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation with combined power-type nonlinearities
    • preprint math.AP/0511070
    • Tao T., Visan M., Zhang X.: The nonlinear Schrödinger equation with combined power-type nonlinearities, preprint math.AP/0511070
    • Tao, T.1    Visan, M.2    Zhang, X.3
  • 38
    • 79551645226 scopus 로고    scopus 로고
    • Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in higher dimensions
    • preprint math.AP/0609692
    • Tao T., Visan M., Zhang X.: Global well-posedness and scattering for the mass-critical nonlinear Schrödinger equation for radial data in higher dimensions, preprint math.AP/0609692
    • Tao, T.1    Visan, M.2    Zhang, X.3
  • 39
    • 0000237067 scopus 로고
    • 2-solutions for nonlinear Schrödinger equations and nonlinear groups
    • 2-solutions for nonlinear Schrödinger equations and nonlinear groups. Funkcial Ekvac. 30 (1987), 115-125
    • (1987) Funkcial Ekvac , vol.30 , pp. 115-125
    • Tsutsumi, Y.1
  • 40
    • 0035379526 scopus 로고    scopus 로고
    • Regularity of solutions to the free Schrödinger equation with radial initial data
    • Vilela M.: Regularity of solutions to the free Schrödinger equation with radial initial data. Illinois J. Math. 45 (2001), 361-370
    • (2001) Illinois J. Math , vol.45 , pp. 361-370
    • Vilela, M.1
  • 41
    • 34547304016 scopus 로고    scopus 로고
    • The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
    • to appear
    • Visan M.: The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions, to appear Duke Math. J.
    • Duke Math. J
    • Visan, M.1
  • 42
    • 55549142795 scopus 로고    scopus 로고
    • Visan M, The defocusing energy-critical nonlinear Schrödinger equation in dimensions five and higher. Ph.D. thesis
    • Visan M.: The defocusing energy-critical nonlinear Schrödinger equation in dimensions five and higher. Ph.D. thesis
  • 43
    • 55549086436 scopus 로고    scopus 로고
    • 2-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class
    • preprint math.AP/0606737
    • 2-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class, preprint math.AP/0606737
    • Visan, M.1    Zhang, X.2
  • 44
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • Weinstein M.: 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.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.