Yukawa-type system

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

Global well posedness in the energy class (H¹,H¹xL²) 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 (H^s,H^mxH^{m − 1}) whenever and s + m > 3 / 2Pe-p2.