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arXiv · 2403.12824

Well-posedness and no-uniform dependence for the Euler-Poincar\'{e} equations in Triebel-Lizorkin spaces

Yuanhua Zhong·Jianzhong Lu·Min Li·Jinlu Li
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Abstract

In this paper, we study the Cauchy problem of the Euler-Poincar\'{e} equations in $\R^d$ with initial data belonging to the Triebel-Lizorkin spaces. We prove the local-in-time unique existence of solutions to the Euler-Poincar\'{e} equations in $F^s_{p,r}(\R^d)$. Furthermore, we obtain that the data-to-solution of this equation is continuous but not uniformly continuous in these spaces.

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Yuanhua Zhong, Jianzhong Lu, Min Li, Jinlu Li. 2024-03-19. Well-posedness and no-uniform dependence for the Euler-Poincar\'{e} equations in Triebel-Lizorkin spaces. https://arxiv.org/abs/2403.12824

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