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<p>In this paper, we prove the uniqueness of globally conservative solutions for a class of nonlinear dispersive wave equations by the analysis of characteristics. Giving a conservative solution, we introduce a set of auxiliary variables tailored to this solution, and prove that these variables satisfy a suitable semilinear system of equations. By proving that this semilinear system has a unique solution, we eventually obtain the uniqueness of the conservative solution to the original equation.</p>

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Uniqueness of globally conservative weak solutions for a class of nonlinear dispersive wave equations beyond wave breaking

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Yonghui Zhou,
  • Xiaowan Li

摘要

In this paper, we prove the uniqueness of globally conservative solutions for a class of nonlinear dispersive wave equations by the analysis of characteristics. Giving a conservative solution, we introduce a set of auxiliary variables tailored to this solution, and prove that these variables satisfy a suitable semilinear system of equations. By proving that this semilinear system has a unique solution, we eventually obtain the uniqueness of the conservative solution to the original equation.