We study the dispersive properties of the linear Schr¨odinger equation with a timedependent potential V (t, x). We show that an appropriate integrability condition in space and time on V , i.e. the boundedness of a suitable L^r L^s 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 ∈ L^rL^s.
Some remarks on the Schroedinger equation with a potential in L^r_tL^s_x
VISCIGLIA, NICOLA
2005-01-01
Abstract
We study the dispersive properties of the linear Schr¨odinger equation with a timedependent potential V (t, x). We show that an appropriate integrability condition in space and time on V , i.e. the boundedness of a suitable L^r L^s 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 ∈ L^rL^s.File in questo prodotto:
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