Potentiels variables et équations dispersives

Marius Beceanu[1]

  • [1] Department of Mathematics University of California, Berkeley 970 Evans Hall Berkeley, CA 94720-3840

Séminaire Laurent Schwartz — EDP et applications (2012-2013)

  • page 1-11
  • ISSN: 2266-0607

How to cite

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Beceanu, Marius. "Potentiels variables et équations dispersives." Séminaire Laurent Schwartz — EDP et applications (2012-2013): 1-11. <http://eudml.org/doc/275707>.

@article{Beceanu2012-2013,
affiliation = {Department of Mathematics University of California, Berkeley 970 Evans Hall Berkeley, CA 94720-3840},
author = {Beceanu, Marius},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {fre},
pages = {1-11},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Potentiels variables et équations dispersives},
url = {http://eudml.org/doc/275707},
year = {2012-2013},
}

TY - JOUR
AU - Beceanu, Marius
TI - Potentiels variables et équations dispersives
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2012-2013
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 11
LA - fre
UR - http://eudml.org/doc/275707
ER -

References

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  1. 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. Zbl0315.47007MR397194
  2. M. Beceanu, A structure formula for wave operators on 3 , to appear in AJM. Zbl06293185
  3. M. Beceanu, New estimates for a time-dependent Schrödinger equation, Duke Math. J. 159, 3 (2011), pp. 351–559. Zbl1229.35224MR2831875
  4. M. Beceanu, A. Soffer, The Schrödinger equation with a potential in rough motion, Comm. PDE, 37 :6, 969-1000. Zbl1245.35099MR2924464
  5. J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, 1976. Zbl0344.46071MR482275
  6. J. Bourgain, Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential, Commun. Math. Phys. 204, pp. 207–247 (1999). Zbl0938.35150MR1705671
  7. J. Bourgain, On growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential, J. Anal. Math. 77, 315–348 (1999). Zbl0938.35026MR1753490
  8. 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. Zbl1071.35038MR2083390
  9. M. Christ, A. Kiselev, Maximal operators associated to filtrations, J. Funct. Anal. 179 (2001), pp. 409–425. Zbl0974.47025MR1809116
  10. O. Costin, J. L. Lebowitz, S. Tanveer, Ionization of Coulomb systems in 3 by time periodic forcing of arbitrary size, Comm. Math. Phys. 296 (2010), no. 3, pp. 681–738. Zbl1209.37087MR2628820
  11. 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). Zbl1229.35040MR2652223
  12. 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. Zbl1247.35118MR2915755
  13. 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. Zbl1138.81018MR2083143
  14. M. Goldberg, Strichartz estimates for the Schrödinger equation with time-periodic L n / 2 potentials, J. Funct. Anal., Vol. 256, Issue 3, 2009, pp. 718–746. Zbl1161.35004MR2484934
  15. A. D. Ionescu, W. Schlag, Agmon–Kato–Kuroda theorems for a large class of perturbations, Duke Math. J. 131, 3 (2006), pp. 397–591. Zbl1092.35073MR2219246
  16. M. Keel, T. Tao, Endpoint Strichartz estimates, Amer. Math. J. 120 (1998), pp. 955–980. Zbl0922.35028MR1646048
  17. 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. Zbl1063.35035MR2038194
  18. E. Stein, Harmonic Analysis, Princeton University Press, Princeton, 1994. Zbl0821.42001
  19. W.-M. Wang, Logarithmic bounds on Sobolev norms for time dependent linear Schrödinger equations, Commun. Partial Differ. Equ. 33, pp. 2164–2179 (2008). Zbl1154.35450MR2475334
  20. K. Yajima, The W k , p -continuity of wave operators for Schrödinger operators, J. Math. Soc. Japan 47 (1995), pp. 551–581. Zbl0837.35039MR1331331

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