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.
@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},
zbl = {1043.35137},
mrnumber = {1655515},
language = {en},
url = {http://www.numdam.org/item/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://www.numdam.org/item/ASNSP_1997_4_25_1-2_197_0/

[Bo] J. Bourgain, On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE, International Math. Res. Notices 6 (1996), 277-304. | MR 1386079 | Zbl 0934.35166

[G] R. Glassey, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger operators, J. Math. Phys. 8 (1977), 1794-1797. | MR 460850 | Zbl 0372.35009

[GV] J. Ginibre - G. Velo, 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 533218 | Zbl 0396.35028

[Ka] T. Kato, On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Physique Theorique 46 (1987), 113-129. | EuDML 76348 | Numdam | MR 877998 | Zbl 0632.35038

[Kw] M. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in RN, Arch. Rat. Mech. Anal. 105 (1989), 243-266. | Zbl 0676.35032

[M1] F. Merle, Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power, Duke Math. J. 69 (1993), 427-453. | MR 1203233 | Zbl 0808.35141

[M2] F. Merle, 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 1048692

[M3] F. Merle, Limit of the solution of a nonlinear Schrödinger equation at blow-up time, J. Functional Anal. 84 (1989), 201-214. | MR 999497 | Zbl 0681.35078

[MT] F. Merle - Y. Tsutsumi, L2 concentration of blow-up solutions for the nonlinear Schrödingerequation with critical power nonlinearity, J. Diff. Eq. 84 (1990), 205-214. | MR 1047566 | Zbl 0722.35047

[N] H. Nawa, Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity, J. Math. Soc. Japan 46 (1994), 557-586. | MR 1291107 | Zbl 0829.35121

[SSP] P.L. Sulem - C. Sulem - A. Patera, Numerical simulations ofsingular solutions to the two-dimensional cubic Schrödinger equation, J. Comp. Phus. 37 (1984), 755-778. | MR 762872 | Zbl 0543.65081

[Wein] M. Weinstein, On the structure and formation of singularities in solutions to the nonlinear dispersive evolution equation, Comm. PDE 11 (1986), 545-565. | MR 829596 | Zbl 0596.35022

[Wein1]M. Weinstein, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16 (1985), 472-491. | MR 783974 | Zbl 0583.35028

[Wein2] M. Weinstein, 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 1034501 | Zbl 0703.35159

[Z] V. Zakharov - V. Synakh, The nature of self-focusing singularity, Zh. Eksp. Teir. Fiz. 68 (1975), 940-947; Sov. Phys. JETP 41 (1975), 465-468.