Uniqueness and generic regularity of global weak conservative solutions to the Constantin-Lannes equation
Uniqueness and generic regularity of global weak conservative solutions to the Constantin-Lannes equation
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DOI：
10.1080/00036811.2022.2107912
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发表时间：
2022-08
影响因子：
1.1
通讯作者：
Li Yang;Shouming Zhou;Hongying Yang
中科院分区：
文献类型：
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作者：
Li Yang;Shouming Zhou;Hongying Yang
本文研究中振幅方程(Constantin-Lannes方程)浅水波整体时间守恒解的唯一性和一般正则性。Constantin-Lannes方程可能在有限时间内发生奇性发展，并且在波破裂发生之后，它存在整体守恒解。在这篇文章中，我们将通过分析量u的演化和每个特征，证明具有一般初始数据的Constantin-Lannes方程的全局时间守恒解的唯一性。此外，我们还考虑了只有一般奇性的分段光滑解在Thom横截性引理的整个解集上是稠密的。
ABSTRACT This paper is devoted to the uniqueness of global-in-time conservative solutions and generic regularity for the shallow water waves of moderate amplitude equation (Constantin-Lannes equation). The Constantin-Lannes equation possible development of singularities in finite time, and beyond the occurrence of wave breaking, it exists global conservative solutions. In the present paper, we will prove the uniqueness of global-in-time conservative solutions for the Constantin-Lannes equation with general initial data by analyzing the evolution of the quantities u and along each characteristic. Moreover, we consider that piecewise smooth solutions with only generic singularities are dense in the whole solution set by Thom's transversality Lemma.