| 日時 | 1月 9日(金) 16:15--17:15 |
|---|---|
| 講師 | Piero D'Ancona 氏 (Univ. Roma) |
| 題目 | Almost optimal local well posedness for the Maxwell-Dirac system |
| 概要 | in a joint work with Damiano Foschi and Sigmund Selberg, we recently closed a long-standing conjecture concerning the MD system, namely the local well posedness in $ H^s \times H^{s-1/2} $ (spinor field x electromagnetic field) for all $ s>0 $. Recall that $ L^2 \times \dot H^{-1/2} $ is the scale invariant space for the system. Notable features of this result are: 1) we work in the Lorentz gauge, which was previously considered a "bad"gauge for MD and MKG but in fact turned out to be the correct one; 2) previous results on MD did not uncover the full null structure of the system. To get it, it is necessary to keep into account the full algebraic structure of the system and embed it in suitable tri- and quadrilinear estimates. 3) we follow the standard iteration method in suitable wave-Sobolev spaces, however new refined estimates involving angular decompositions are necessary to close the iteration. |