论文标题
Camassa-Holm方程的Peamons的稳定性超越波浪破裂
Stability of peakons of the Camassa-Holm equation beyond wave breaking
论文作者
论文摘要
使用一个广义框架，该框架包括camassa-Holm方程的解决方案及其能量度量的发展，我们建立了峰山峰的全球轨道稳定性，相对于扰动的（能量）保守解决方案对Camassa-Holm方程。尤其是，即使在扰动的解决方案体验波浪破裂之后，我们也扩展了康斯坦丁和Strauss（Comm。PureAppl。Math。，53（5），603-610，2000）获得的H1稳定性结果。此外，我们的结果还表明，扰动溶液的能量度量的奇异部分将始终保持稳定。
Using a generalized framework that consists of evolution of the solution to the Camassa- Holm equation and its energy measure, we establish the global-in-time orbital stability of peakons with respect to the perturbed (energy) conservative solutions to the Camassa-Holm equation. Especially, we extend the H1-stability result obtained by Constantin and Strauss (Comm. Pure Appl. Math., 53(5), 603-610, 2000) globally-in-time, even after the perturbed solutions experience wave breaking. In addition, our result also shows that the singular part of the energy measure of the perturbed solutions will remain stable for all times.
