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Strichartz estimates for charge transfer models
Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, IL 60615, USA |
In this note, we prove Strichartz estimates for scattering states of scalar charge transfer models in $\mathbb{R}^{3}$. Following the idea of Strichartz estimates based on [
References:
[1] |
K. Cai, Fine properties of charge transfer models, preprint, arXiv: math/0311048. |
[2] |
S. Cuccagna,
Stabilization of solutions to nonlinear Schrödinger equations, Comm. Pure Appl. Math., 54 (2001), 1110-1145.
doi: 10.1002/cpa.1018. |
[3] |
S. Cuccagna and M. Maeda,
On weak interaction between a ground state and a non-textendashtrapping potential, J. Differential Equations, 256 (2014), 1395-1466.
doi: 10.1016/j.jde.2013.11.002. |
[4] |
M. B. Erdogan and W. Schlag,
Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: Ⅱ, J. Anal. Math., 99 (2006), 199-248.
doi: 10.1007/BF02789446. |
[5] |
J. M. Graf,
Phase space analysis of the charge transfer model, Helv. Physica Acta, 63 (1990), 107-138.
|
[6] |
J.-L. Journe, A. Soffer and C. D. Sogge,
Decay estimates for Schrödinger operators, Comm. Pure Appl. Math., 44 (1991), 573-604.
doi: 10.1002/cpa.3160440504. |
[7] |
M. Keel and T. Tao,
Endpoint Strichartz estimates, Amer. J. Math., 120 (1998), 955-980.
doi: 10.1353/ajm.1998.0039. |
[8] |
L. Linares and G. Ponce,
Introduction to Nonlinear Dispersive Equations Universitext. Springer, New York, 2009.
doi: 978-0-387-84898-3. |
[9] |
I. Rodnianski and W. Schlag,
Time decay for solutions of Schrödinger equations with rough and time-dependent potentials, Invent. Math., 155 (2004), 451-513.
doi: 10.1007/s00222-003-0325-4. |
[10] |
I. Rodnianski, W. Schlag and A. Soffer,
Dispersive analysis of charge transfer models, Comm. Pure Appl. Math., 58 (2005), 149-216.
doi: 10.1002/cpa.20066. |
[11] |
W. Schlag, Dispersive estimates for Schrödinger operators: A survey, in Mathematical aspects of nonlinear dispersive equations, Ann. of Math. Stud. , (eds. J. Bourgain, C. Kenig and S. Klainerman), Princeton Univ. Press, 163 (2007), 255-285. |
[12] |
K. Yajima,
The Wk, p-continuity of wave operators for Schrödinger operators, J. Math. Soc. Japan, 47 (1995), 551-581.
doi: 10.2969/jmsj/04730551. |
[13] |
K. Yajima,
A multichannel scattering theory for some time dependent Hamiltonians, charge transfer problem, Comm. Math. Phys., 75 (1980), 153-178.
doi: 10.1007/BF01222515. |
show all references
References:
[1] |
K. Cai, Fine properties of charge transfer models, preprint, arXiv: math/0311048. |
[2] |
S. Cuccagna,
Stabilization of solutions to nonlinear Schrödinger equations, Comm. Pure Appl. Math., 54 (2001), 1110-1145.
doi: 10.1002/cpa.1018. |
[3] |
S. Cuccagna and M. Maeda,
On weak interaction between a ground state and a non-textendashtrapping potential, J. Differential Equations, 256 (2014), 1395-1466.
doi: 10.1016/j.jde.2013.11.002. |
[4] |
M. B. Erdogan and W. Schlag,
Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: Ⅱ, J. Anal. Math., 99 (2006), 199-248.
doi: 10.1007/BF02789446. |
[5] |
J. M. Graf,
Phase space analysis of the charge transfer model, Helv. Physica Acta, 63 (1990), 107-138.
|
[6] |
J.-L. Journe, A. Soffer and C. D. Sogge,
Decay estimates for Schrödinger operators, Comm. Pure Appl. Math., 44 (1991), 573-604.
doi: 10.1002/cpa.3160440504. |
[7] |
M. Keel and T. Tao,
Endpoint Strichartz estimates, Amer. J. Math., 120 (1998), 955-980.
doi: 10.1353/ajm.1998.0039. |
[8] |
L. Linares and G. Ponce,
Introduction to Nonlinear Dispersive Equations Universitext. Springer, New York, 2009.
doi: 978-0-387-84898-3. |
[9] |
I. Rodnianski and W. Schlag,
Time decay for solutions of Schrödinger equations with rough and time-dependent potentials, Invent. Math., 155 (2004), 451-513.
doi: 10.1007/s00222-003-0325-4. |
[10] |
I. Rodnianski, W. Schlag and A. Soffer,
Dispersive analysis of charge transfer models, Comm. Pure Appl. Math., 58 (2005), 149-216.
doi: 10.1002/cpa.20066. |
[11] |
W. Schlag, Dispersive estimates for Schrödinger operators: A survey, in Mathematical aspects of nonlinear dispersive equations, Ann. of Math. Stud. , (eds. J. Bourgain, C. Kenig and S. Klainerman), Princeton Univ. Press, 163 (2007), 255-285. |
[12] |
K. Yajima,
The Wk, p-continuity of wave operators for Schrödinger operators, J. Math. Soc. Japan, 47 (1995), 551-581.
doi: 10.2969/jmsj/04730551. |
[13] |
K. Yajima,
A multichannel scattering theory for some time dependent Hamiltonians, charge transfer problem, Comm. Math. Phys., 75 (1980), 153-178.
doi: 10.1007/BF01222515. |
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