Well-Posedness for a Nonlinear Schrödinger Equation with Quadratic Derivative Nonlinearities for Bounded Primitive Initial Data

抄録

We consider the Cauchy problem for a quadratic derivative nonlinear Schrödinger equation whose nonlinearity is a linear combination of ∂_x(u²) and ∂_x(|u|²). We prove the local well-posedness in the L²-based Sobolev space H^s(R) for s ≥ 0 with bounded primitives. Moreover, we prove the global well-posedness in H^s(R) for s ≥ 1 and a special case of the coefficients of nonlinearities.