Null structure in a system of quadratic derivative nonlinear Schrödinger equations

Abstract

We consider the initial value problem for a three-component system of quadratic derivative nonlinear Schrödinger 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.

33 pages

References in corpus (1)

• A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D

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