Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincar\'e equations

Wei Luo; Zhaoyang Yin

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arXiv · 1810.07993

Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincar\'e equations

Wei Luo·Zhaoyang Yin

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Abstract

In this paper we mainly investigate the initial value problem of the periodic Euler-Poincar\'e 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-Poincar\'e equations is 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.

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Wei Luo, Zhaoyang Yin. 2018-10-18. Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincar\'e equations. https://arxiv.org/abs/1810.07993

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