Random Data Cauchy Problem for Supercritical Schrödinger Equations
Thomann, Laurent
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 2385-2402 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2009__26_6_2385_0,
     author = {Thomann, Laurent},
     title = {Random Data Cauchy Problem for Supercritical Schr\"odinger Equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {2385-2402},
     doi = {10.1016/j.anihpc.2009.06.001},
     mrnumber = {2569900},
     zbl = {1180.35491},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2385_0}
}

Thomann, Laurent. Random Data Cauchy Problem for Supercritical Schrödinger Equations. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2385-2402. doi : 10.1016/j.anihpc.2009.06.001. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2385_0/

[1] Bourgain J., Periodic Nonlinear Schrödinger Equation and Invariant Measures, Comm. Math. Phys. 166 (1994) 1-26. | MR 1309539 | Zbl 0822.35126

[2] Bourgain J., Invariant Measures for the 2D-Defocusing Nonlinear Schrödinger Equation, Comm. Math. Phys. 176 (1996) 421-445. | MR 1374420 | Zbl 0852.35131

[3] N. Burq, L. Thomann, N. Tzvetkov, Gibbs measures for the nonlinear harmonic oscillator, preprint.

[4] Burq N., Tzvetkov N., Invariant Measure for the Three-Dimensional Nonlinear Wave Equation, Int. Math. Res. Not. IMRN 22 (2007), Art. ID rnm108, 26 pp. | Zbl 1134.35076

[5] Burq N., Tzvetkov N., Random Data Cauchy Theory for Supercritical Wave Equations I: Local Existence Theory, Invent. Math. 173 (3) (2008) 449-475. | MR 2425133 | Zbl 1156.35062

[6] Burq N., Tzvetkov N., Random Data Cauchy Theory for Supercritical Wave Equations II: a Global Existence Result, Invent. Math. 173 (3) (2008) 477-496. | MR 2425134 | Zbl pre05314912

[7] Carles R., Geometric Optics and Instability for Semi-Classical Schrödinger Equations, Arch. Ration. Mech. Anal. 183 (3) (2007) 525-553. | MR 2278414 | Zbl 1134.35098

[8] Carles R., Rotating Points for the Conformal NLS Scattering Operator, Dyn. Partial Differ. Equ. 6 (1) (2009) 35-51. | MR 2517827 | Zbl pre05608745

[9] Carles R., Linear Vs. Nonlinear Effects for Nonlinear Schrödinger Equations With Potential, in: Contemp. Math., vol. 7(4), 2005, pp. 483-508. | MR 2166662 | Zbl 1095.35044

[10] Ginibre J., Velo G., On a Class of Nonlinear Schrödinger Equations, J. Funct. Anal. 32 (1) (1979) 1-71. | MR 533219 | Zbl 0396.35029

[11] Keel M., Tao T., Endpoint Strichartz Estimates, Amer. J. Math. 120 (5) (1998) 955-980. | MR 1646048 | Zbl 0922.35028

[12] Koch H., Tataru D., L p Eigenfunction Bounds for the Hermite Operator, Duke Math. J. 128 (2) (2005) 369-392. | MR 2140267 | Zbl 1075.35020

[13] Taylor M. E., Tools for PDE. Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, Math. Surveys Monogr., vol. 81, American Mathematical Society, Providence, RI, 2000. | MR 1766415 | Zbl 0963.35211

[14] Thomann L., Instabilities for Supercritical Schrödinger Equations in Analytic Manifolds, J. Differential Equations 245 (1) (2008) 249-280. | MR 2422717 | Zbl 1157.35107

[15] N. Tzvetkov, Construction of a Gibbs measure associated to the periodic Benjamin-Ono equation, Probab. Theory Related Fields, in press. | MR 2574736 | Zbl pre05668292

[16] Tzvetkov N., Invariant Measures for the Defocusing NLS, Ann. Inst. Fourier 58 (2008) 2543-2604. | Numdam | MR 2498359 | Zbl 1171.35116

[17] Tzvetkov N., Invariant Measures for the Nonlinear Schrödinger Equation on the Disc, Dyn. Partial Differ. Equ. 3 (2006) 111-160. | MR 2227040 | Zbl 1142.35090

[18] Yajima K., Zhang G., Local Smoothing Property and Strichartz Inequality for Schrödinger Equations With Potentials Superquadratic at Infinity, J. Differential Equations 1 (2004) 81-110. | MR 2060533 | Zbl 1060.35121

[19] Yajima K., Zhang G., Smoothing Property for Schrödinger Equations With Potential Superquadratic at Infinity, Comm. Math. Phys. 221 (3) (2001) 573-590. | MR 1852054 | Zbl 1102.35320

[20] Zhidkov P., KdV and Nonlinear Schrödinger Equations: Qualitative Theory, Lecture Notes in Math., vol. 1756, Springer, 2001. | MR 1831831 | Zbl 0987.35001