Davey-Stewartson系统在低能量空间中的整体适定性

Global Well-Posedness Results for Davey-Stewartson Systems Below the Energy Norm

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.

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.