Logarithmic bounds on Sobolev norms for time-dependent linear Schrödinger equations

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dc.creatorWang, W. -M.
dc.date2008-05-24
dc.date2008-09-30
dc.date.accessioned2026-07-07T10:05:55Z
dc.date.available2026-07-07T10:05:55Z
dc.descriptionWe prove that in 1-D the growth of Sobolev norms for time-dependent linear Schrödinger equations is at most logarithmic in time for any (fixed) potential which is analytic (or Gevrey). Recently it was proven in [N] that almost surely the Sobolev norms are unbounded, which indicates that the log is almost surely necessary. In [W], the author showed that the Sobolev norms remain bounded for an explicit time periodic potential. This is in the exceptional set in the sense of [N]. The present paper together with [N, W] give a rather complete picture of time dependent linear Schrödinger equations on the circle.
dc.descriptionTo appear in Commun. PDE (2008)
dc.identifierhttps://arxiv.org/abs/0805.3771
dc.identifierhttp://arxiv.org/abs/0805.3771
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170155
dc.subjectSpectral Theory
dc.subjectAnalysis of PDEs
dc.subject35xx
dc.titleLogarithmic bounds on Sobolev norms for time-dependent linear Schrödinger equations
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