【摘要】 得到了具粗糙初值的Davey-Stewartson系统的整体适定性,具体地说,证明了当初值在Sobolev空间H~s(s>2/3)中的整体解的存在性,即解可能具有无限能量.证明的创新在于应用Bourgain提出的Fourier限制方法及分频技术,同时得到了解的H~s范数关于时间的增长可由一多项式函数控制.更多还原

【Abstract】 The global well-posedness for the Davey-Stewartson systems is obtained with rough data.More precisely the authors show that a global solution exists for initial data in the Sobolev space H~s and any s>2/3,then the initial data may have infinite energy.The new ingredient in the proof is to apply the Fourier restriction norm method of Bourgain by showing a generalized estimates of Strichartz type and splitting the data into low and high frequency parts.A byproduct of the method is that the H~s norm of the solution obeys polynomial-in-time bounds.更多还原