Local Well-Posedness for the Derivative Nonlinear Schrödinger Equations with $L^2$ Subcritical Data

Shaoming Guo, Xianfeng Ren, Baoxiang Wang

We will show its local well-posedness in modulation spaces $M^{1/2}_{2,q}({\Real})$ $(2\le q<\infty )$. It is well-known that $H^{1/2}$ is a critical Sobolev space of DNLS so that…