Some remarks on the Schrödinger equation with a potential in L^r_tL^s_x

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• 作者：Piero D' Ancona ; Vittoria Pierfelice and Nicola Visciglia
• 关键词：Mathematics Subject Classification (2000) 35B40 ; 35B25 ; 35B65 ; 35Q40 ; 35Q55
• 刊名：Mathematische Annalen
• 出版年：2005
• 出版时间：October 2005
• 年：2005
• 卷：333
• 期：2
• 页码：271-290
• 全文大小：213 KB

文摘

We study the dispersive properties of the linear Schr?dinger 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_tLs_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_tLs_x.