On the blowup theory for the critical nonlinear Schrödinger equations
- [1] IRMAR, Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex France
Séminaire Équations aux dérivées partielles (2004-2005)
- Volume: 2004-2005, page 1-8
Access Full Article
topHow to cite
topKeraani, Sahbi. "On the blowup theory for the critical nonlinear Schrödinger equations." Séminaire Équations aux dérivées partielles 2004-2005 (2004-2005): 1-8. <http://eudml.org/doc/11111>.
@article{Keraani2004-2005,
affiliation = {IRMAR, Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex France},
author = {Keraani, Sahbi},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-8},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On the blowup theory for the critical nonlinear Schrödinger equations},
url = {http://eudml.org/doc/11111},
volume = {2004-2005},
year = {2004-2005},
}
TY - JOUR
AU - Keraani, Sahbi
TI - On the blowup theory for the critical nonlinear Schrödinger equations
JO - Séminaire Équations aux dérivées partielles
PY - 2004-2005
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2004-2005
SP - 1
EP - 8
LA - eng
UR - http://eudml.org/doc/11111
ER -
References
top- H. Bahouri and P. Gérard: High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math. 121 (1999), no. 1, 131–175. Zbl0919.35089MR1705001
- V. Banica: Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004), no. 1, 139–170. Zbl1170.35528MR2064970
- T. Cazenave: Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003. Zbl1055.35003MR2002047
- P. Gérard: Description du défaut de compacité de l’injection de Sobolev, ESAIM.COCV, Vol 3, (1998) 213-233. Zbl0907.46027
- J. Ginibre, G. Velo: On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case, J. Funct. Anal. 32 (1979), no. 1, 1–32. Zbl0396.35028MR533218
- R.T. Glassey : On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys. 18 (1977), no. 9, 1794–1797. Zbl0372.35009MR460850
- S. Keraani: On the defect of compactness for the Strichartz estimates of the Schrödinger equations, J. Differential Equations 175 (2001), no. 2, 353–392. Zbl1038.35119MR1855973
- M.K. Kwong: uniqueness of positive solutions to , in , Arch. Rat. Mech. Anal 105 (1989), n. 3, 243-266. Zbl0676.35032MR969899
- P-L. Lions: The concentration-compactness principle in the calculus of variations. The compact case. Part 1, Ann. Inst. Henri Poincaré, Analyse non linéaire 1 (1984), 109-145. MR778970
- F. Merle: Determination of blowup solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J. 69, (1993),no. 2, 203-254. Zbl0808.35141MR1203233
- —: Construction of solutions with exactly blowup points for nonlinear Schrödinger equations with critical nonlinearity, Comm.Math. Phys. 129 (1990), no.2, 223-240. Zbl0707.35021MR1048692
- —: Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations. Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Doc. Math. 1998, Extra Vol. III, 57–66 Zbl0896.35123MR1648140
- F. Merle, Y. Tsutsumi: concentration of blowup solutions for the nonlinear Schrödinger equation with critical power nonlinearity, J. Differential Equations 84 (1990), no. 2, 205–214. Zbl0722.35047MR1047566
- C. Sulem, P-L. Sulem: The nonlinear Schrödinger equation. Self-focusing and wave collapse, Applied Mathematical Sciences, 139. Springer-Verlag, New York, 1999. Zbl0928.35157MR1696311
- Y. Tsutsumi: Rate of concentration of blowup solutions for the nonlinear Schr̦dinger equation with critical power, Nonlinear Anal. 15 (1990), no. 8, 719–724. Zbl0726.35124MR1074950
- M. I. Weinstein: Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Physi. 87 (1983), 567-567. Zbl0527.35023MR691044
- —: On the structure of singularities in solutions to the nonlinear dispersive evolution equations, Comm. Partial Differential Equations, 11 (1984), 545-565. Zbl0596.35022
- —: The nonlinear Schrödinger equation—singularity formation, stability and dispersion. The connection between infinite-dimensional and finite-dimensional dynamical systems, Contemp. Math., 99, Amer. Math. Soc., Providence, RI, 1989, 213–232. Zbl0703.35159MR1034501
NotesEmbed ?
topComment withdrawn
Comment withdrawn
Comment withdrawn
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.