Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger Equations
Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger Equations
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DOI：
10.1016/j.jfa.2012.04.010
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发表时间：
2012-07
影响因子：
1.7
通讯作者：
Takeshi Wada
中科院分区：
文献类型：
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作者：
Takeshi Wada
我们考虑R1+ 2中带有电磁势的薛定谔方程。势属于H1，并且通常它们是时间无关的或被确定为非齐次波动方程的解。我们证明了Kato型光滑估计的解决方案。我们也将这个结果应用到Lorentz规范中的Maxwell-Schr dinger方程，并证明了这个系统在能量空间中的唯一可解性。
We consider Schrödinger equations in R1+2with electro-magnetic potentials. The potentials belong to H1, 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–Schrödinger equations in the Lorentz gauge and prove unique solvability of this system in the energy space.