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arXiv · 1811.00375

Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations

Jinlu Li·Zhaoyang Yin·Weipeng Zhu
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Abstract

In this paper, we establish the continuous dependence for the non-resistive MHD equations in Sobolev spaces. Our obtained result fills considerably the recent result [C. Fefferman, D. McCormick, J. Robinson and J. Rodrigo, Higher order commutator estimates and local existence for the non-resistive MHD equations and related models, J. Funct. Anal. 267 (2014), 1035--1056] for the continuous dependence on initial data. We also show that this result is optimal. More precisely, we proved that the data-to-solution map is not uniform continuous dependence in Sobolev spaces.

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Jinlu Li, Zhaoyang Yin, Weipeng Zhu. 2018-11-01. Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations. https://arxiv.org/abs/1811.00375

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