| 一类弱耗散Camassa-Holm方程局部强解的适定性及弱解的存在性 |
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| 引用本文： | 赖绍永,吴永洪. 一类弱耗散Camassa-Holm方程局部强解的适定性及弱解的存在性[J]. 中国科学:数学, 2010, 40(9): 901-920 |
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| 作者姓名： | 赖绍永 吴永洪 |
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| 作者单位： | 1. 西南财经大学应用数学系, 成都610074;
2. Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia |
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| 基金项目： | 教育部科学技术研究重点项目（批准号：109140）资助 |
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| 摘 要： | 使用Pseudoparabolic正则化方法和从弱耗散Camassa-Holm方程自身导出的估计式,在Sobolev空间Hs(R)(s3/2)中,证明了该Camassa-Holm方程解的局部适定性.同时给出了一个在空间Hs(R)(1s23)中确保该方程弱解存在的充分条件.
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| 关 键 词： | 局部适定性 耗散Camassa-Holm方程 高阶非线性项 弱解 |
Local well-posedness and weak solutions for a weakly dissipative Camassa-Holm equation |
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| LAI ShaoYong ＆ WU YongHong. Local well-posedness and weak solutions for a weakly dissipative Camassa-Holm equation[J]. Scientia Sinica Mathemation, 2010, 40(9): 901-920 |
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| Authors: | LAI ShaoYong ＆ WU YongHong |
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| Affiliation: | LAI ShaoYong ＆ WU YongHong |
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| Abstract: | The local well-posedness of solutions for a weakly dissipative Camassa-Holm equation in the Sobolev space Hs （R） with s 〉 3 is established by using the pseudoparabolic regularization technique and some estimates derived from the equation itself. A sufficient condition which guarantees the existence of weak solutions for the equation in lower order Sobolev space Hs with 1〈s≤3/2 is developed. |
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| Keywords: | local well-posedness dissipative Camassa-Holm equation high order nonlinear terms weak solutions |
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