Yukawa-type system

i u_t + D u = -A u Box A = m2 A + |u|2

for d=3. A represents the meson field, while u is the nucleon field.

Global well posedness in the energy class (H1, H1 x L2) is in [Bch1984], [BlChd1978], [FuTs1978], [HaWl1987]. Modified wave operators were constructed for large energy data at infinity in [GiVl-p2].

With positive mass m=1, global well-posedness can be pushed to (Hs, Hm x Hm-1) whenever 1 ³ s,m > 7/10 and s+m > 3/2 [Pe-p2].