Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
Anne de Bouard; Nakao Hayashi; Keiichi Kato
Annales de l'I.H.P. Analyse non linéaire (1995)
- Volume: 12, Issue: 6, page 673-725
- ISSN: 0294-1449
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topde Bouard, Anne, Hayashi, Nakao, and 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 12.6 (1995): 673-725. <http://eudml.org/doc/78371>.
@article{deBouard1995,
author = {de Bouard, Anne, Hayashi, Nakao, Kato, Keiichi},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {generalized Korteweg-de Vries equation; nonlinear Schrödinger equations; initial function; Gevrey class},
language = {eng},
number = {6},
pages = {673-725},
publisher = {Gauthier-Villars},
title = {Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations},
url = {http://eudml.org/doc/78371},
volume = {12},
year = {1995},
}
TY - JOUR
AU - de Bouard, Anne
AU - Hayashi, Nakao
AU - Kato, Keiichi
TI - Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 6
SP - 673
EP - 725
LA - eng
KW - generalized Korteweg-de Vries equation; nonlinear Schrödinger equations; initial function; Gevrey class
UR - http://eudml.org/doc/78371
ER -
References
top- [A] H. Aikawa, Infinite order Sobolev spaces, analytic continuation and polynomial expansions, Complex Variables, Vol. 18, 1992, pp. 253-266. Zbl0767.46023MR1157933
- [B] A. De Bouard, Analytic solutions to nonelliptic nonlinear Schrödinger equations, J. Diff. Eqs., Vol. 104, 1993, pp. 196-213. Zbl0798.35138MR1224127
- [Co-Sau] P. Constantin and J.C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., Vol. 1, 1988, pp. 413-439. Zbl0667.35061MR928265
- [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. Zbl0764.35021MR1160847
- [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. Zbl0396.35028MR533219
- [H] N. Hayashi, Analyticity of solutions of the Korteweg-de Vries equation, SIAM J. Math. Anal., Vol. 22, 1991, pp. 1738-1745. Zbl0742.35056MR1129407
- [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. Zbl0617.35025MR847012
- [H-K.K] N. Hayashi and K. Kato, Regularity of solutions in time to nonlinear Schrödinger equations, J. Funct. Anal., 1994 (to appear). Zbl0876.35108MR1319956
- [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. Zbl0803.35137MR1255899
- [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. Zbl0705.35132MR1046275
- [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. Zbl0549.34001MR759907
- [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. Zbl0622.35066MR870865
- [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. Zbl0738.35022MR1101221
- [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. Zbl0786.35121MR1230709
- [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. Zbl0808.35128MR1211741
- [Ko] H. Komatsu, "Introduction to distributions, ultradistributions and hyperfunctions (in Japanese)", IwanamiKisosugaku, 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. Zbl0549.35104MR691986
- [L] C. Laurey, The Cauchy problem for a third order nolinear Schrödinger equations, preprint, 1993. MR1446222
- [P] G. Ponce, Regularity of solutions to nonlinear dispersive equations, J. Diff. Eqs., Vol. 78, 1989, pp. 122-135. Zbl0699.35036MR986156
- [Sj] P. Sjölin, Regularity of solutions to the Schrödinger equations, Duke Math. J., Vol. 55, 1987, pp. 699-715. Zbl0631.42010MR904948
- [St] W. Strauss, Dispersion of low energy waves for two conservative equations, Arch. Rational Mech. Anal., Vol. 55, 1974, pp. 86-92. Zbl0289.35048MR352743
- [V] L. Vega, Schrödinger equations : pointwise convergence to the initial data, Proc. Amer. Math. Soc., Vol. 102, pp. 874-878. Zbl0654.42014MR934859
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