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On the Cauchy problem for the XFEL Schrödinger equation

  • * Corresponding author: Binhua Feng

    * Corresponding author: Binhua Feng 
This work is supported by NSFC Grants (No. 11601435, No. 11475073), Gansu Provincial Natural Science Foundation (1606RJZA010) and NWNU-LKQN-14-6.
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  • In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equation with a time-dependent electromagnetic field and a Coulomb potential, which arises as an effective single particle model in X-ray free electron lasers(XFEL). We firstly show the local and global well-posedness for the Cauchy problem under the assumption that the magnetic potential is unbounded and time-dependent, and then obtain the regularity by a fixed point argument.

    Mathematics Subject Classification: 35Q51, 35Q55.


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