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

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 u0∈Hs(R)∩W2,∞(R)(1≤s≤2). Firstly, we deduce an ODE system, whose equivalence to problem (1.2) with a spatial initial condition will be...

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Published in:Journal of mathematical analysis and applications 2020-03, Vol.483 (2), p.123633, Article 123633
Main Authors: Zhang, Yuanyuan, Hu, Qiaoyi
Format: Article
Language:English
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Camassa-Holm equation
Cubic nonlinearity
Flow
Weak well-posedness
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description 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 u0∈Hs(R)∩W2,∞(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.
doi_str_mv 10.1016/j.jmaa.2019.123633
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subjects Camassa-Holm equation
Cubic nonlinearity
Flow
Weak well-posedness
title Weak well-posedness for the integrable modified Camassa-Holm equation with the cubic nonlinearity
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