The Cauchy problem for a two-component Novikov equation in the critical Besov space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:423

Article

Tang, Hao¹  Liu, Zhengrong¹ 

[1] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China

关键词: Two-component Novikov equation;    Cauchy problem;    Besov spaces;    Local well-posedness;   

DOI  :  10.1016/j.jmaa.2014.09.032

来源: Elsevier

【 摘 要 】

In this paper, we consider the Cauchy problem for a two-component Novikov equation in the critical Besov space B-2,1(5/2). We first derive a new a priori estimate for the 1-D transport equation in B-2,infinity(3/2) which is the endpoint case. Then we apply this a priori estimate and the Osgood lemma to prove the local existence. Moreover, we also show that the solution map no u(0) -> u is Holder continuous in B-2,1(5/2) equipped with weaker topology. It is worth mentioning that our method is different from the previous one that involves extracting a convergent subsequence from an iterative sequence in critical Besov spaces. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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