Strichartz estimates for charge transfer models

Gong Chen

doi:10.3934/dcds.2017050

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2017, Volume 37, Issue 3: 1201-1226. Doi: 10.3934/dcds.2017050

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Strichartz estimates for charge transfer models

Gong Chen

Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, IL 60615, USA

Received: September 30, 2015

Revised: October 31, 2016

Published: May 2017

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Abstract

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 [3,10], we also show that the energy of the whole evolution is bounded independently of time without using the phase space method, as for example, in [5]. One can easily generalize our arguments to $\mathbb{R}^{n}$ for $n≥q3$ . We also discuss the extension of these results to matrix charge transfer models in $\mathbb{R}^{3}$ .

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Mathematics Subject Classification: Primary:35Q35, 37K40.

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References

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