| 杨晗,杨宁.Davey-Stewartson系统在低能量空间中的整体适定性[J].数学年刊A辑,2009,30(5):685~696 |
| 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 |
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| DOI： |
| 中文关键词: Davey-Stewartson系统 整体适定性 Strichartz估计 Fourier截断方法 |
| 英文关键词:Davey-Stewartson systems, Global well-posedness, Strichartz
estimates, Fourier truncation method |
| 基金项目:国家自然科学基金，西南交通大学基础研究基金(No.2007B05)资助的项目 |
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| 中文摘要: |
| 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Hs(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Hs范数关于时间的增长可由一多项式函数控制. |
| 英文摘要: |
| 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 $s>\frac{2}{3}$, 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. |
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