Global solutions for small nonlinear long range perturbations of two dimensional Schrödinger equations  [ Solutions globales pour des perturbations nonlinéaires à longue portée de l’équation de Schrödinger en dimension 2 ] (2002)


Delort, Jean-Marc
Mémoires de la Société Mathématique de France, Tome 91 (2002) vi-94 p doi : 10.24033/msmf.404
URL stable : http://www.numdam.org/item?id=MSMF_2002_2_91__1_0

Bibliographie

[1] J.-M. BonyCalcul symbolique et propagation des singularités pour les équations aux dérivées partielles nonlinéaires, Ann. Scient. Éc. Norm. Sup. 14, (1981) 209–256. | MR 631751

[2] A. P. Calderón & R. VaillancourtOn the boundedness of pseudo-differential operators, J. Math. Soc. Japan 23, (1971), 374–378. Zbl 0203.45903 | MR 284872

[3] J.-Y. CheminFluides parfaits incompressibles, Astérisque 230, (1995). MR 1340046

[4] H. ChiharaLocal existence for semi-linear Schrödinger equations, Math. Japonica 42, (1995), 35–52. MR 1344627

[5] —, Global existence of small solutions to semi-linear Schrödinger equations, Comm. Partial Differential Equations 21, (1996), 63–78. Zbl 0843.35111 | MR 1373765

[6] —, The initial value problem for cubic semi-linear Schrödinger equations, Publ. RIMS, Kyoto Univ. 32, (1996), 445–471. Zbl 0870.35095 | MR 1409797

[7] S. CohnGlobal existence for the nonresonant Schrödinger equation in two space dimensions, Canad. Appl. Math. Quart. 2, (1994), 247-282. MR 1318545

[8] J.-M. DelortExistence globale et comportement asymptotique pour l’équation de Klein-Gordon quasi linéaire à données petites en dimension 1, Ann. Scient. Éc. Norm. Sup. 34, (2001), 1–61. | MR 1833089

[9] S. DoiOn the Cauchy problem for Schrödinger type equations and the regularity of the solutions, J. Math. Kyoto Univ. 34, (1994), 319–328. Zbl 0807.35026 | MR 1284428

[10] N. Hayashi & H. HirataGlobal existence of small solutions to nonlinear Schrödinger equations, Nonlinear Analysis, Theory, Methods and Applications 31, (1998), 671–685. Zbl 0886.35141 | MR 1487854

[11] N. Hayashi & K. KatoGlobal existence of small analytic solutions to Schrödinger equations with quadratic nonlinearities, Comm. Partial Differential Equations 22, (1997), 773–798. Zbl 0881.35106 | MR 1452167

[12] N. Hayashi, C. Miao & P.I. NaumkinGlobal existence of small solutions to the generalized derivative nonlinear Schrödinger equation, Asymptotic Analysis 21, (1999), 133–147. Zbl 0937.35171 | MR 1723555

[13] N. Hayashi & P.I. NaumkinOn the quadratic nonlinear Schrödinger equation in three space dimensions, Internat. Math. Res. Notices (2000), 115–132. Zbl 1004.35112 | MR 1741610

[14] —, Asymptotics of small solutions to nonlinear Schrödinger equations with cubic nonlinearities, preprint, 12 pp.

[15] —, Global existence of small solutions to the quadratic nonlinear Schrödinger equation in two space dimensions, SIAM J. Math. Anal. 32 (2001), no. 6, 1390–1409.

[16] —, Asymptotic expansion of small analytic solutions to the quadratic nonlinear Schrödinger equation in two space dimensions, preprint, 15 pp.

[17] —, A quadratic nonlinear Schrödinger equation in one space dimension, preprint, 18 pp.

[18] N. Hayashi & T. OzawaRemarks on nonlinear Schrödinger equations in one space dimension, Diff. Integral Eqs 7, (1994), 453–461. Zbl 0803.35137 | MR 1255899

[19] C. Kenig, G. Ponce & L. VegaSmall solutions to nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré 10, (1993), 255–288. Numdam | Zbl 0786.35121 | | MR 1230709

[20] —, Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations, Invent. Math. 134 (1998), no. 3, 489–545. Zbl 0928.35158 | MR 1660933