| WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES |
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| 作者姓名： | HUO Zhaohui JIA Yueling |
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| 作者单位： | HUO ZHAOHUI JIA YUELING Graduate School，China Academy of Engineering Physics，P. O. Box 2101，Beijing 100088，China. Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China. |
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| 摘 要： | The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s≥-1/4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s > 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.
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| 关 键 词： | 傅里叶限制范数 三线估计 希罗塔方程 柯西问题 低正则 偏微分方程 |
| 收稿时间： | 2003/11/3 0:00:00 |
WELL-POSEDNESS FOR THE CAUCHY PROBLEM
TO THE HIROTA EQUATION IN SOBOLEV
SPACES OF NEGATIVE INDICES |
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| HUO Zhaohui,JIA Yueling.WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES[J].Chinese Annals of Mathematics,Series B,2005,26(1):75-88. |
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| Authors: | HUO Zhaohui and JIA Yueling |
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| Institution: | 1. Graduate School,China Academy of Engineering Physics,P. O.Box 2101,Beijing,100088,China
2. Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing,100080,China |
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| Abstract: | The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s ≥ -1-4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s ＞ 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method. |
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| Keywords: | Fourier restriction norm Trilinear estimates Hirota equation Low regularity Global well-posedness |
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