Abstract
We improve Delort’s method to show that solutions of linear Schrödinger equations with a time dependent Gevrey potential on the torus, have at most logarithmically growing Sobolev norms. In particular, it contains the result of Wang (Commun Partial Differ Equ 33:2164–2179, 2008), which deals with analytic potentials in dimension 1.
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Fang, D., Zhang, Q. On Growth of Sobolev Norms in Linear Schrödinger Equations with Time Dependent Gevrey Potential. J Dyn Diff Equat 24, 151–180 (2012). https://doi.org/10.1007/s10884-012-9244-7
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DOI: https://doi.org/10.1007/s10884-012-9244-7