 01369 I. Rodnianski, W. Schlag
 Time decay for solutions of Schr\"odinger equations with rough and time dependent potentials
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Oct 12, 01

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Abstract. We establish dispersive and Strichartz estimates for solutions to the
linear timedependent Schr\"odinger equations with potential in three
dimensions. Our main focus is on the small rough timedependent potentials.
Examples of such potentials are of the form $V(t,x)=T(t) V_0(x)$, where
$T$ is quasiperiodic in time and $V_0$ is essentially an $L^{3/2}$
function of the spatial variables. We also prove the dispersive estimates
for small timeindependent potentials which belong to the interestion of
the Rollnik and global Kato classes.
Finally, we settle the question posed by Journe, Soffer, Sogge concerning
Strichartz estimates for potentials that decay faster than $x^{2}$ in
dimensions greater or equal to three.
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