@article{ASNSP_1997_4_25_1-2_197_0, author = {Bourgain, Jean and Wang, W.}, title = {Construction of blowup solutions for the nonlinear {Schr\"odinger} equation with critical nonlinearity}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {197--215}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 25}, number = {1-2}, year = {1997}, mrnumber = {1655515}, zbl = {1043.35137}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1997_4_25_1-2_197_0/} }
TY - JOUR AU - Bourgain, Jean AU - Wang, W. TI - Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1997 SP - 197 EP - 215 VL - 25 IS - 1-2 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1997_4_25_1-2_197_0/ LA - en ID - ASNSP_1997_4_25_1-2_197_0 ER -
%0 Journal Article %A Bourgain, Jean %A Wang, W. %T Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1997 %P 197-215 %V 25 %N 1-2 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1997_4_25_1-2_197_0/ %G en %F ASNSP_1997_4_25_1-2_197_0
Bourgain, Jean; Wang, W. Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 197-215. http://archive.numdam.org/item/ASNSP_1997_4_25_1-2_197_0/
[Bo] On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE, International Math. Res. Notices 6 (1996), 277-304. | MR | Zbl
,[G] On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger operators, J. Math. Phys. 8 (1977), 1794-1797. | MR | Zbl
,[GV] On a class of nonlinear Schrödinger equations I. The Cauchy problem, general case; II. Scattering theory, general case, J. Func. Anal. 32 (1979), 1-71. | MR | Zbl
- ,[Ka] On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Physique Theorique 46 (1987), 113-129. | EuDML | Numdam | MR | Zbl
,[Kw] Uniqueness of positive solutions of Δu - u + up = 0 in RN, Arch. Rat. Mech. Anal. 105 (1989), 243-266. | Zbl
,[M1] Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power, Duke Math. J. 69 (1993), 427-453. | MR | Zbl
,[M2] Construction of solutions with exact k blow-up points for the Schrödinger equation with critical power nonlinearity, Comm. Math. Phys. 149 (1992), 205-214. | MR
,[M3] Limit of the solution of a nonlinear Schrödinger equation at blow-up time, J. Functional Anal. 84 (1989), 201-214. | MR | Zbl
,[MT] L2 concentration of blow-up solutions for the nonlinear Schrödingerequation with critical power nonlinearity, J. Diff. Eq. 84 (1990), 205-214. | MR | Zbl
- ,[N] Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity, J. Math. Soc. Japan 46 (1994), 557-586. | MR | Zbl
,[SSP] Numerical simulations ofsingular solutions to the two-dimensional cubic Schrödinger equation, J. Comp. Phus. 37 (1984), 755-778. | MR | Zbl
- - ,[Wein] On the structure and formation of singularities in solutions to the nonlinear dispersive evolution equation, Comm. PDE 11 (1986), 545-565. | MR | Zbl
,[Wein1]Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16 (1985), 472-491. | MR | Zbl
,[Wein2] The nonlinear Schrödinger equation: singularity formation stability and dispersion, in "AMS-SIAM conference on the connection between infinite dimensional and finite dimensional dynamical systems" (1987), 25-40. | MR | Zbl
,[Z] The nature of self-focusing singularity, Zh. Eksp. Teir. Fiz. 68 (1975), 940-947; Sov. Phys. JETP 41 (1975), 465-468.
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