Abstract
We study the dispersive properties of the linear Schrödinger equation with a time-dependent potential V(t,x). We show that an appropriate integrability condition in space and time on V, i.e. the boundedness of a suitable Lr t Ls x norm, is sufficient to prove the full set of Strichartz estimates. We also construct several counterexamples which show that our assumptions are optimal, both for local and for global Strichartz estimates, in the class of large unsigned potentials V ∈Lr t Ls x .
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Support. The authors are partially supported by the Research Training Network (RTN) HYKE and by grant HPRN-CT-2002-00282 from the European Union. The third author is supported also by INDAM
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Ancona, P., Pierfelice, V. & Visciglia, N. Some remarks on the Schrödinger equation with a potential in Lr t Ls x . Math. Ann. 333, 271–290 (2005). https://doi.org/10.1007/s00208-005-0672-0
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DOI: https://doi.org/10.1007/s00208-005-0672-0