Weak well-posedness for the integrable modified Camassa-Holm equation with the cubic nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Zhang, Yuanyuan¹  Hu, Qiaoyi¹ 

[1] South China Agr Univ, Dept Math, Guangzhou 510642, Guangdong, Peoples R China

关键词: Camassa-Holm equation;    Cubic nonlinearity;    Weak well-posedness;    Flow;   

DOI  :  10.1016/j.jmaa.2019.123633

来源: Elsevier

【 摘 要 】

The goal of this paper is supposed to investigate the weak well-posedness for the modified Camassa-Holm equation with cubic nonlinearity after given an initial data u(0) is an element of H-s(R) boolean AND W-2,W-infinity(R) (1 <= s <= 2). Firstly, we deduce an ODE system, whose equivalence to problem (1.2) with a spatial initial condition will be verified later. Next, by studying the existence of the unique solution to the ODE system, we conclude the corresponding results of the original problem. Finally, we end up with the weak continuity of solutions to the PDE associated to the initial datum. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free