@article{SLSEDP_2012-2013____A19_0, author = {Marius Beceanu}, title = {Potentiels variables et \'equations dispersives}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:19}, pages = {1--11}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2012-2013}, doi = {10.5802/slsedp.45}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.45/} }
TY - JOUR AU - Marius Beceanu TI - Potentiels variables et équations dispersives JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:19 PY - 2012-2013 SP - 1 EP - 11 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.45/ DO - 10.5802/slsedp.45 LA - fr ID - SLSEDP_2012-2013____A19_0 ER -
%0 Journal Article %A Marius Beceanu %T Potentiels variables et équations dispersives %J Séminaire Laurent Schwartz — EDP et applications %Z talk:19 %D 2012-2013 %P 1-11 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.45/ %R 10.5802/slsedp.45 %G fr %F SLSEDP_2012-2013____A19_0
Marius Beceanu. Potentiels variables et équations dispersives. Séminaire Laurent Schwartz — EDP et applications (2012-2013), Talk no. 19, 11 p. doi : 10.5802/slsedp.45. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.45/
[Agm] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), No. 2, pp. 151–218. | Numdam | MR | Zbl
[Bec1] M. Beceanu, A structure formula for wave operators on , to appear in AJM.
[Bec2] M. Beceanu, New estimates for a time-dependent Schrödinger equation, Duke Math. J. 159, 3 (2011), pp. 351–559. | MR | Zbl
[BeSo] M. Beceanu, A. Soffer, The Schrödinger equation with a potential in rough motion, Comm. PDE, 37 :6, 969-1000. | MR | Zbl
[BeLö] J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, 1976. | MR | Zbl
[Bou1] J. Bourgain, Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential, Commun. Math. Phys. 204, pp. 207–247 (1999). | MR | Zbl
[Bou2] J. Bourgain, On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential, J. Anal. Math. 77, 315–348 (1999). | MR | Zbl
[Bou3] J. Bourgain, On long-time behaviour of solutions of linear Schrödinger equations with smooth time-dependent potential, Geometric aspects of functional analysis, pp. 99–113, Lecture Notes in Math., 1807, Springer, Berlin, 2003. | MR | Zbl
[ChKi] M. Christ, A. Kiselev, Maximal operators associated to filtrations, J. Funct. Anal. 179 (2001), pp. 409–425. | MR | Zbl
[CLT] O. Costin, J. L. Lebowitz, S. Tanveer, Ionization of Coulomb systems in by time periodic forcing of arbitrary size, Comm. Math. Phys. 296 (2010), no. 3, pp. 681–738. | MR | Zbl
[Del] J.-M. Delort, Growth of Sobolev norms of solutions of linear Schrödinger equations on some compact manifolds, Int. Math. Res. Not. 12, pp. 2305–2328 (2010). | MR | Zbl
[FaZh] D. Fang, Q. Zhang, On Growth of Sobolev Norms in Linear Schrödinger Equations with Time Dependent Gevrey Potential, Journal of Dynamics and Differential Equations, June 2012, Volume 24, Issue 2, pp. 151–180. | MR | Zbl
[GJY] A. Galtbayar, A. Jensen, K. Yajima, Local time-decay of solutions to Schrödinger equations with time-periodic potentials, Journal of Statistical Physics, Vol. 116, No. 1–4, 2004, pp. 231–282. | MR | Zbl
[Gol] M. Goldberg, Strichartz estimates for the Schrödinger equation with time-periodic potentials, J. Funct. Anal., Vol. 256, Issue 3, 2009, pp. 718–746. | MR | Zbl
[IoSc] A. D. Ionescu, W. Schlag, Agmon–Kato–Kuroda theorems for a large class of perturbations, Duke Math. J. 131, 3 (2006), pp. 397–591. | MR | Zbl
[KeTa] M. Keel, T. Tao, Endpoint Strichartz estimates, Amer. Math. J. 120 (1998), pp. 955–980. | MR | Zbl
[RoSc] I. Rodnianski, W. Schlag, Time decay for solutions of Schrödinger equations with rough and time-dependent potentials, Invent. Math. 155 (2004), no. 3, pp. 451–513. | MR | Zbl
[Ste] E. Stein, Harmonic Analysis, Princeton University Press, Princeton, 1994. | Zbl
[Wan] W.-M. Wang, Logarithmic bounds on Sobolev norms for time dependent linear Schrödinger equations, Commun. Partial Differ. Equ. 33, pp. 2164–2179 (2008). | MR | Zbl
[Yaj] K. Yajima, The -continuity of wave operators for Schrödinger operators, J. Math. Soc. Japan 47 (1995), pp. 551–581. | MR | Zbl
Cited by Sources: