On the Blow-up Phenomena of Cauchy Problem for the Camassa-Holm Equation  

作　　者：LIU Yongqin WANG Weike 

机构地区：[1]School of Mathematics and Statistics, Wuhan Universily, Wuhan 430072, Hubei, China [2]Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China

出　　处：《Wuhan University Journal of Natural Sciences》2006年第3期451-455,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foun-dation of China (10131050) ;Science and Technology Committee of Shanghai ,China (03JC14013)

摘　　要：We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.

关 键 词：WAVE-BREAKING blow-up rate blow-up set 

分 类 号：O175.29[理学—数学]