Null structure in a system of quadratic derivative nonlinear Schrödinger equations

Masahiro Ikeda, Soichiro Katayama, Hideaki Sunagawa

Published 2013-05-16Version 1

We consider the initial value problem for a three-component system of quadratic derivative nonlinear Schr\"odinger equations in two space dimensions with the masses satisfying the resonance relation. We present a structural condition on the nonlinearity under which small data global existence holds. It is also shown that the solution is asymptotically free. Our proof is based on the commuting vector field method combined with smoothing effects.