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Main Authors: Zhong, Yuanhua, Lu, Jianzhong, Li, Min, Li, Jinlu
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.12824
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author Zhong, Yuanhua
Lu, Jianzhong
Li, Min
Li, Jinlu
author_facet Zhong, Yuanhua
Lu, Jianzhong
Li, Min
Li, Jinlu
contents In this paper, we study the Cauchy problem of the Euler-Poincaré 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-Poincaré 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_12824
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces
Zhong, Yuanhua
Lu, Jianzhong
Li, Min
Li, Jinlu
Analysis of PDEs
35Q35
In this paper, we study the Cauchy problem of the Euler-Poincaré 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-Poincaré 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.
title Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces
topic Analysis of PDEs
35Q35
url https://arxiv.org/abs/2403.12824