Local Well-posedness of the Derivative Schr?dinger Equation in Higher Dimension for Any Large Data

【摘要】：In this paper,the authors consider the local well-posedness for the derivative Schr?dinger equation in higher dimension■ It is shown that the Cauchy problem of the derivative Schr?dinger equation in higher dimension is locally well-posed in H~s(R~n)(sn/2) for any large initial data.Thus this result can compare with that in one dimension except for the endpoint space H~(n/2).