一个n分支 μ-Camassa-Holm系统解的局部适定性和爆破现象研究

Local Well-Posedness and Blow-Up Phenomena of Solutions of a n-Component μ-Camassa-Holm System

首先利用Kato理论,研究了一个具有多尖峰孤子解和满足H1守恒的n分支μ-Camassa-Holm系统Cauchy问题解的局部适定性;然后利用守恒律和能量估计,研究了该系统解的爆破现象。By utilizing Kato theory, this paper first establishes the local well-posedness of the solutions of the Cauchy problem of a n-component μ-Camassa-Holm system with multi-peakons and H1-conservation law. Then, the blow-up phenomena of the solutions is studied by means of conservation law and energy estimations.