@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] Periodic Nonlinear Schrödinger Equation and Invariant Measures, Comm. Math. Phys. 166 (1994) 1-26. | MR | Zbl
,[2] 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] Invariant Measure for the Three-Dimensional Nonlinear Wave Equation, Int. Math. Res. Not. IMRN 22 (2007), Art. ID rnm108, 26 pp. | Zbl
, ,[5] Random Data Cauchy Theory for Supercritical Wave Equations I: Local Existence Theory, Invent. Math. 173 (3) (2008) 449-475. | MR | Zbl
, ,[6] Random Data Cauchy Theory for Supercritical Wave Equations II: a Global Existence Result, Invent. Math. 173 (3) (2008) 477-496. | MR
, ,[7] Geometric Optics and Instability for Semi-Classical Schrödinger Equations, Arch. Ration. Mech. Anal. 183 (3) (2007) 525-553. | MR | Zbl
,[8] Rotating Points for the Conformal NLS Scattering Operator, Dyn. Partial Differ. Equ. 6 (1) (2009) 35-51. | MR
,[9] Linear Vs. Nonlinear Effects for Nonlinear Schrödinger Equations With Potential, in: Contemp. Math., vol. 7(4), 2005, pp. 483-508. | MR | Zbl
,[10] On a Class of Nonlinear Schrödinger Equations, J. Funct. Anal. 32 (1) (1979) 1-71. | MR | Zbl
, ,[11] Endpoint Strichartz Estimates, Amer. J. Math. 120 (5) (1998) 955-980. | MR | Zbl
, ,[12] Eigenfunction Bounds for the Hermite Operator, Duke Math. J. 128 (2) (2005) 369-392. | MR | Zbl
, ,[13] Tools for PDE. Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials, Math. Surveys Monogr., vol. 81, American Mathematical Society, Providence, RI, 2000. | MR | Zbl
,[14] 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] Invariant Measures for the Defocusing NLS, Ann. Inst. Fourier 58 (2008) 2543-2604. | Numdam | MR | Zbl
,[17] Invariant Measures for the Nonlinear Schrödinger Equation on the Disc, Dyn. Partial Differ. Equ. 3 (2006) 111-160. | MR | Zbl
,[18] Local Smoothing Property and Strichartz Inequality for Schrödinger Equations With Potentials Superquadratic at Infinity, J. Differential Equations 1 (2004) 81-110. | MR | Zbl
, ,[19] Smoothing Property for Schrödinger Equations With Potential Superquadratic at Infinity, Comm. Math. Phys. 221 (3) (2001) 573-590. | MR | Zbl
, ,[20] KdV and Nonlinear Schrödinger Equations: Qualitative Theory, Lecture Notes in Math., vol. 1756, Springer, 2001. | MR | Zbl
,Cité par Sources :