Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
de Bouard, Anne ; Hayashi, Nakao ; Kato, Keiichi
Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995), p. 673-725 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_1995__12_6_673_0,
     author = {de Bouard, Anne and Hayashi, Nakao and Kato, Keiichi},
     title = {Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schr\"odinger equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {12},
     year = {1995},
     pages = {673-725},
     mrnumber = {1360541},
     zbl = {0843.35098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1995__12_6_673_0}
}

de Bouard, Anne; Hayashi, Nakao; Kato, Keiichi. Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations. Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) pp. 673-725. http://gdmltest.u-ga.fr/item/AIHPC_1995__12_6_673_0/

[A] H. Aikawa, Infinite order Sobolev spaces, analytic continuation and polynomial expansions, Complex Variables, Vol. 18, 1992, pp. 253-266. | MR 1157933 | Zbl 0767.46023

[B] A. De Bouard, Analytic solutions to nonelliptic nonlinear Schrödinger equations, J. Diff. Eqs., Vol. 104, 1993, pp. 196-213. | MR 1224127 | Zbl 0798.35138

[Co-Sau] P. Constantin and J.C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., Vol. 1, 1988, pp. 413-439. | MR 928265 | Zbl 0667.35061

[Cr-Kap-St] W. Craig, K. Kappeler and W.A. Strauss, Gain of regularity for solutions of KdV type, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 9, 1992, pp. 147-186. | Numdam | MR 1160847 | Zbl 0764.35021

[G-Vel] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations I, II, J. Funct. Anal., Vol. 32, 1979, pp. 1-32, 33-71. | MR 533219 | Zbl 0396.35028

[H] N. Hayashi, Analyticity of solutions of the Korteweg-de Vries equation, SIAM J. Math. Anal., Vol. 22, 1991, pp. 1738-1745. | MR 1129407 | Zbl 0742.35056

[H-N-T] N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equation in one space dimension, Math. Z., Vol. 192, 1986, pp. 637-650. | MR 847012 | Zbl 0617.35025

[H-K.K] N. Hayashi and K. Kato, Regularity of solutions in time to nonlinear Schrödinger equations, J. Funct. Anal., 1994 (to appear). | MR 1319956 | Zbl 0876.35108

[H-O] N. Hayashi and T. Ozawa, Remarks on nonlinear Schrödinger equations in one space dimensions, Diff. and Integral Eqs., Vol. 7, 1994, pp. 453-461. | MR 1255899 | Zbl 0803.35137

[H-Sai] N. Hayashi and S. Saitoh, Analyticity and global existence of small solutions to some nonlinear Schrödinger equations, Commun. Math. Phys., Vol. 129, 1990, pp. 27-42. | MR 1046275 | Zbl 0705.35132

[Ka] T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Stud. Appl. Math. Adv. in Math. Supplementary Studies, Vol. 18, 1983, pp. 93-128. | MR 759907 | Zbl 0549.34001

[Ka-M] T. Kato and K. Masuda, Nonlinear evolution equations and analyticity I, Ann. Inst. Henri Poincaré Analyse non linéaire, Vol. 3, 1986, pp. 455-467. | Numdam | MR 870865 | Zbl 0622.35066

[Ke-P-V 1] C.E. Kenig, G. Ponce and L. Vegaa, Oscillatory integrals and regularity of dipersive equations, Indiana Univ. Math. J., Vol. 40, 1991, pp. 33-69. | MR 1101221 | Zbl 0738.35022

[Ke-P-V 2] C.E. Kenig, G. Ponce and L. Vegaa, Small solutions to nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 10, 1993, pp. 255-288. | Numdam | MR 1230709 | Zbl 0786.35121

[Ke-P-V 3] C.E. Kenig, G. Ponce and L. Vegaa, Higher order non-linear dispersive equations, preprint, 1992.

[Ke-P-V 4] C.E. Kenig, G. Ponce and L. Vegaa, On the hierarchy of the generalized KdV equations, Proc. Lyon Workshop on Singular Limits of Dispersive Waves, 1993 (to appear).

[Ke-P-V 5] C.E. Kenig, G. Ponce and L. Vegaa, Well-posedness and scattering results for the generalized Korteweg-de Vries equations via the contraction principle, Comm. Pure. Appl. Math., Vol. 46, 1993, pp. 527-620. | MR 1211741 | Zbl 0808.35128

[Ko] H. Komatsu, "Introduction to distributions, ultradistributions and hyperfunctions (in Japanese)", Iwanami Kisosugaku, Iwanami shoten, Tokyo, 1978.

[Kr-F] S.N. Kruzhkov and A.V. Faminskii, Generalized solutions to the Cauchy problem for the Korteweg-de Vries equation, Math. U.S.S.R. Sbornik, Vol. 48, 1984, pp. 93-138. | MR 691986 | Zbl 0549.35104

[L] C. Laurey, The Cauchy problem for a third order nolinear Schrödinger equations, preprint, 1993. | MR 1446222

[P] G. Ponce, Regularity of solutions to nonlinear dispersive equations, J. Diff. Eqs., Vol. 78, 1989, pp. 122-135. | MR 986156 | Zbl 0699.35036

[Sj] P. Sjölin, Regularity of solutions to the Schrödinger equations, Duke Math. J., Vol. 55, 1987, pp. 699-715. | MR 904948 | Zbl 0631.42010

[St] W. Strauss, Dispersion of low energy waves for two conservative equations, Arch. Rational Mech. Anal., Vol. 55, 1974, pp. 86-92. | MR 352743 | Zbl 0289.35048

[V] L. Vega, Schrödinger equations : pointwise convergence to the initial data, Proc. Amer. Math. Soc., Vol. 102, pp. 874-878. | MR 934859 | Zbl 0654.42014