Gevrey regularizing effect for a nonlinear Schrödinger equation in one space dimension

Kazuo TANIGUCHI

doi:10.2969/jmsj/05041015

Kazuo TANIGUCHI

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JOURNAL FREE ACCESS

1998 Volume 50 Issue 4 Pages 1015-1026

DOI https://doi.org/10.2969/jmsj/05041015

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Published: 1998 Received: August 31, 1996 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. De Bouard, N. Hayashi and K. Kato, Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Analse non linéaire, 12 (1995), 673-725.
2) H. Chihara, Local existence for the semilinear Schrödinger equations in one space dimension, J. Math. Kyoto Univ., 34 (1994), 353-367.
3) N. Hayashi and K. Kato, Regularity in time of solutions to nonlinear Schrödinger equations, J. Funct. Anal., 128 (1995), 253-277.
4) N. Hayashi and T. Ozawa, Remarks on nonlinear Schrödinger equations in one space dimension, Diff: Integral Eqs., 7 (1994), 453-461.
5) K. Kato and K. Taniguchi, Gevrey regularizing effect for nonlinear Schrödinger equations, Osaka J. Math., 33 (1996), 863-880.
6) S. Mizohata, On some Schrödinger type equations, Proc. Japan Acad., 57 (1981), 81-84.
7) S. Mizohata, Sur quelques équations du type Schrödinger, Journées “Équations aux Dérivées Partielles”. Soc. Math. France, 1981.
8) J. Takeuchi, On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots, J. Math. Kyoto Univ., 20 (1980), 105-124.
9) J. Takeuchi, Some remarks on my paper “On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots”. J. Math. Kyoto Univ., 24 (1984), 741-754.

Right : [1] A. De Bouard, N. Hayashi and K. Kato, Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Analse non linéaire, 12 (1995), 673-725.
[2] H. Chihara, Local existence for the semilinear Schrödinger equations in one space dimension, J. Math. Kyoto Univ., 34 (1994), 353-367.
[3] N. Hayashi and K. Kato, Regularity in time of solutions to nonlinear Schrödinger equations, J. Funct. Anal., 128 (1995), 253-277.
[4] N. Hayashi and T. Ozawa, Remarks on nonlinear Schrödinger equations in one space dimension, Diff. Integral Eqs., 7 (1994), 453-461.
[5] K. Kato and K. Taniguchi, Gevrey regularizing effect for nonlinear Schrödinger equations, Osaka J. Math., 33 (1996), 863-880.
[6] S. Mizohata, On some Schrödinger type equations, Proc. Japan Acad., 57 (1981), 81-84.
[7] S. Mizohata, Sur quelques équations du type Schrödinger, Journées “Équations aux Dérivées Partielles”. Soc. Math. France, 1981.
[8] J. Takeuchi, On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots, J. Math. Kyoto Univ., 20 (1980), 105-124.
[9] J. Takeuchi, Some remarks on my paper “On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots”, J. Math. Kyoto Univ., 24 (1984), 741-754.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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