Date | Nov 21, 2023 |
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Speaker | 양창훈 |

Dept. | 충북대학교 |

Room | 27-116 |

Time | 16:00-17:00 |

In this talk, we consider the Maxwell-Dirac system in 3 dimensions under zero magnetic field. We prove the global well-posedness and modified scattering for small solutions in the weighted Sobolev class. Imposing the Lorenz gauge condition, and taking the Dirac projection operator, it becomes a system of Dirac equations with Hartree-type nonlinearity with a long-range potential as 1/|x|. We perform the weighted energy estimates. In this procedure, we have to deal with various resonance functions that stem from the Dirac projections. We use the spacetime resonance argument of Germain-Masmoudi-Shatah, as well as the spinorial null structure. On the way, we recognize a long-range interaction that is responsible for a logarithmic phase correction in the modified scattering statement. This talk is based on joint work with Yonggeun Cho, Soonsik Kwon, and Kiyeon Lee.

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