Random Data Cauchy Problem for Supercritical Schrödinger Equations
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2385-2402.
@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},
     pages = {2385--2402},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.06.001},
     mrnumber = {2569900},
     zbl = {1180.35491},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.06.001/}
}
TY  - JOUR
AU  - Thomann, Laurent
TI  - Random Data Cauchy Problem for Supercritical Schrödinger Equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2385
EP  - 2402
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2009.06.001/
DO  - 10.1016/j.anihpc.2009.06.001
LA  - en
ID  - AIHPC_2009__26_6_2385_0
ER  - 
%0 Journal Article
%A Thomann, Laurent
%T Random Data Cauchy Problem for Supercritical Schrödinger Equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2385-2402
%V 26
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2009.06.001/
%R 10.1016/j.anihpc.2009.06.001
%G en
%F 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) no. 6, pp. 2385-2402. doi : 10.1016/j.anihpc.2009.06.001. http://www.numdam.org/articles/10.1016/j.anihpc.2009.06.001/

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

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

[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

[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 | Zbl

[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

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

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

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

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

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

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

[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 | Zbl

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

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

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

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

[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 | Zbl

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

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

Cité par Sources :