分野別セミナー

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.