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arXiv · 2310.09746

Zero-filter limit issue for the Camassa-Holm equation in Besov spaces

Yuxing Cheng·Jianzhong Lu·Min Li·Xing Wu·Jinlu Li
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Abstract

In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of the Camassa-Holm equation converges strongly in $L^\infty(0,T;B^s_{2,r}(\R))$ to the inviscid Burgers equation as the filter parameter $\alpha$ tends to zero with the given initial data $u_0\in B^s_{2,r}(\R)$. Moreover, we also show that the zero-filter limit for the Camassa-Holm equation does not converges uniformly with respect to the initial data in $B^s_{2,r}(\R)$.

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Yuxing Cheng, Jianzhong Lu, Min Li, Xing Wu, Jinlu Li. 2023-10-15. Zero-filter limit issue for the Camassa-Holm equation in Besov spaces. https://arxiv.org/abs/2310.09746

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