高阶双组分Camasss-Holm系统解的Holder连续性

H?lder Continuity for a Two-component High-order Camassa-Holm System

由于高阶双组分Camassa-Holm系统是局部适定的,故该系统的解是连续依赖于初值条件的﹒本文根据局部适定性的结果,利用索伯列夫不等式和能量估计方法,首先给出高阶双组分Camassa-Holm系统解的一个先验估计;然后依据先验估计和索伯列夫插值公式,推导得出高阶双组分Camassa-Holm系统的解是H?lder连续的﹒

From the local well-posedness results of the two-component high-order Camassa-Holm system we know that its solutions depend continuously on their initial data. Based on local well-posedness, we obtain that a priori estimate by Sobolev inequality and energy method. Furthermore, applying interpolation properties of the Sobolev spaces and a priori estimate, we prove that the solution map for the two-component high-order Camassa-Holm system is Holder continuous.