Blow-up phenomena, ill-posedness and peakon solutions for the periodic Euler-Poincare equations
Blow-up phenomena, ill-posedness and peakon solutions for the periodic Euler-Poincare equations
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周期 Euler-Poincare 方程的爆炸现象、不适定性和 Peakon 解
DOI：
10.1016/j.jde.2019.08.042
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发表时间：
2020
影响因子：
2.4
通讯作者：
Yin Zhaoyang
中科院分区：
文献类型：
--
作者：
Luo Wei;Yin Zhaoyang
本文主要研究周期Euler-Poincaré方程的初值问题。首先利用系统的旋转不变性质，对一类特殊的光滑初值问题给出了一个新的爆破结果。然后，通过一个矛盾论证证明了周期Euler-Poincaré方程在临界Besov空间中是不适定的。最后，我们证明了该系统在分布意义下具有一类峰解。
In this paper we mainly investigate the initial value problem of the periodic Euler-Poincaré equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant properties of the system. Then, we prove that the periodic Euler-Poincaré equations are ill-posed in critical Besov spaces by a contradiction argument. Finally, we verify the system possesses a class of peakon solutions in the sense of distributions.