@article{AIHPC_1993__10_3_255_0,
author = {Kenig, Carlos E. and Ponce, Gustavo and Vega, Luis},
title = {Small solutions to nonlinear {Schr\"odinger} equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {255--288},
year = {1993},
publisher = {Gauthier-Villars},
volume = {10},
number = {3},
mrnumber = {1230709},
zbl = {0786.35121},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1993__10_3_255_0/}
}
TY - JOUR AU - Kenig, Carlos E. AU - Ponce, Gustavo AU - Vega, Luis TI - Small solutions to nonlinear Schrödinger equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 1993 SP - 255 EP - 288 VL - 10 IS - 3 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1993__10_3_255_0/ LA - en ID - AIHPC_1993__10_3_255_0 ER -
%0 Journal Article %A Kenig, Carlos E. %A Ponce, Gustavo %A Vega, Luis %T Small solutions to nonlinear Schrödinger equations %J Annales de l'I.H.P. Analyse non linéaire %D 1993 %P 255-288 %V 10 %N 3 %I Gauthier-Villars %U https://www.numdam.org/item/AIHPC_1993__10_3_255_0/ %G en %F AIHPC_1993__10_3_255_0
Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis. Small solutions to nonlinear Schrödinger equations. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 3, pp. 255-288. https://www.numdam.org/item/AIHPC_1993__10_3_255_0/
[1] , Radial Fourier multipliers and associated maximal function, North Holland Math. Studies, III, 1985, pp. 49-55. | Zbl | MR
[2] , An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos, Vol. 22, Universidade Federal do Rio de Janeiro.
[3] and , Some remarks on the nonlinear Schrödinger equation in the critical case, Lecture in Math, Vol. 1392, Springer-Verlag, Berlin, New York, 1989, pp. 18-29. | Zbl | MR
[4] and , Dispersive small amplitude solution to the generalized Korteweg-de Vries equation, J. Funct. Anal., Vol. 100, 1991, pp. 87-109. | Zbl | MR
[5] and , Au-delà des opérateurs pseudo-différentiel, Astérisque, Vol. 57, 1973. | Zbl | Numdam
[6] , and , Local smoothing properties of dispersive equations, J. Amer. Math., Soc., Vol. 1, 1989, pp. 413-446. | Zbl | MR
[7] and , A note an almost every where behavior of solutions to the schrödinger equations, Lecture Notes in Math., Vol. 908, Springer-Verlag, Berlin, New York, 1982, pp. 205-208. | Zbl | MR
[8] , and , Scattering theory in the energy space for a class of nonlinear Schrödinger equation, J. Math. pures et appl., Vol. 64, 1985, pp. 363-401. | Zbl | MR
[9] and , On a class of Schrödinger equations, J. Funct. Anal., Vol. 32, 1979, pp. 1-71. | Zbl | MR
[10] and , Uniqueness for the generalized Korteweg-de Vries equations, SIAM J. Math. Anal., Vol. 20, 1989, pp. 1388-1425. | Zbl | MR
[11] and , On the initial value problem for the Davey-Stewarson systems, Nonlinearity, Vol. 3, 1990, pp. 475-506. | Zbl | MR
[12] , On the blowing up solutions to the Cauchy problem for nonlinar Schrödinger equations, J. Math. Phys., Vol. 18, 1979, pp. 1794-1797. | Zbl | MR
[13] , Global existence of small analytic solutions to nonlinear Schrödinger equations, Duke Math. J, Vol. 62, 1991, pp. 575-592. | MR
[14] , and , On solutions to the initial value problem for the nonlinear Schrödinger equations in one dimensions, Math. Z., Vol. 192, 1986, pp. 637-650. | Zbl | MR
[15] , and , On solutions to the initial value problem for the nonlinear Schrödinger equations, J. Funct. Anal., Vol. 71, 1987, pp. 218-245. | Zbl | MR
[16] and , Analyticity and global existence of small solutions to some nonlinear Shrödinger equations, Comm. Math. Phys., Vol. 129, 1990, pp. 27-41. | Zbl | MR
[17] , Quasilinear evolution equation, with applications to partial differential equations, Lecture Notes in Math., Vol. 448, pringer-Verlag, pp. 27-50.
[18] , Nonlinear Schrödinger equation, Schrodinger operators, H. Holden and A. Jensen Eds, Lecture Notes in Physics, Vol. 345, Springer-Verlag, Berlin, New York, 1989, pp. 218-263. | Zbl
[19] , On the Cauchy problem for the (generalized) Kortewed-de Vries equation, Advances in Math. Supp. Studies, Studies in Applied Math., Vol. 8, 1983, pp. 93-128. | Zbl | MR
[20] and , Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 891-907. | Zbl | MR
[21] and , An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys., Vol. 19, 1978, pp. 798-801. | Zbl | MR
[22] , and , Well-posedness of the initial value problem for the Korteweg-de Vries equation, J. Amer. Math. Soc., Vol. 4, 1991, pp. 323-347. | Zbl | MR
[23] , and , Oscillatory integrals and regularity of dispersive equations, Indiana University Math. J., Vol. 40, 1991, pp. 33-69. | Zbl | MR
[24] , and , On the generalized Benjamin-Ono equation, Trans. Amer. Math. Soc., (to appear). | Zbl | MR
[25] , and , Well-posedness and scattering results for generalized Korteweg-de Vries via contraction principle, Comm. Pure Appl. Math., Vol. 46, 1993, p. 527-620. | Zbl | MR
[26] , and , A strong type (2, 2) estimate for the maximal function associated to the Schrödinger equation, Trans. Amer. Math. Soc., Vol. 280, 1983, pp. 239-246. | Zbl | MR
[27] , Long time behavior of solutions to nonlinear evolutions equations, Arch. Ration. Mech. and Analysis, 78, 1981, pp. 73-98. | Zbl | MR
[28] and , Global small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math., Vol. 36, 1983, pp. 133-141. | Zbl | MR
[29] , Global existence of small solutions to nonlinear evolution equations, J. Diff. Eqs., Vol. 46, 1982, pp. 409-423. | Zbl | MR
[30] and , Wave operators and analytic solutions for systems of systems of nonlinear Klein-Gordon equations and of non-linear Schrödinger equations, Comm. Math. Phys., 99, 1985, pp. 541-562. | Zbl | MR
[31] , Regularity of solutions to the Schrödinger equations, Duke Math., 55, 1987, pp. 699-715. | Zbl | MR
[32] , Oscillaroty integrals in Fourier Analysis, Beijing Lectures in Harmonic Analysis, Princeton University Press, 1986, pp. 307-355. | Zbl | MR
[33] and , Introduction to Fourier Analysis in Eucliden Spaces, Princeton University Press, 1971. | Zbl | MR
[34] , Nonlinear scattering theory at low energy, J. Funct. Anal., 41, 1981, pp. 110-133. | Zbl
[35] , Restriction of Fourier transform to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., Vol. 44, 1977, pp. 705-714. | Zbl | MR
[36] , Global strong solutions for nonlinear Schrödinger equation, Nonlinear Anal., 11, 1987, pp. 1143-1154. | Zbl | MR
[37] , L2-solutions for nonlinear Schrödinger equations and nonlinear groups, Funkcialaj Ekvacioj, Vol. 31, 1987, pp. 115-125. | Zbl | MR
[38] and , On solutions of the derivative nonlinear Schrödinger equation. Existence and Uniqueness Theorem, Funkcialaj Ekvacioj, 23, 1980, pp. 259-277. | Zbl | MR
[39] and , On solutions of the derivative nonlinear Schröndinger equation. II, Funkcialaj Ekvacioj, 24, 1981, pp. 85-94. | Zbl | MR
[40] , Doctoral Thesis, Universidad Autonoma de Madrid, Spain, 1987.
[41] , The Schrödinger eqution: pointwise convergence to the initial date, Proc. Amer. Math. Soc., Vol. 102, 1988, pp. 874-878. | Zbl | MR






