Smoothing effects for Schr枚dinger equations with electro-magnetic potentials and applications to the Maxwell-Schr枚dinger equations

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• 作者：Takeshi Wada¹ ; ^{wada@gpo.kumamoto-u.ac.jp}
• 关键词：Smoothing effect ; Maxwell&ndash ; Schr&ouml ; dinger equations ; Well-posedness
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 July, 2012
• 卷：263
• 期：1
• 页码：1-24
• 文件大小：220 K

摘要

We consider Schr枚dinger equations in with electro-magnetic potentials. The potentials belong to , and typically they are time-independent or determined as solutions to inhomogeneous wave equations. We prove Kato type smoothing estimates for solutions. We also apply this result to the Maxwell-Schr枚dinger equations in the Lorentz gauge and prove unique solvability of this system in the energy space.