Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
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DOI：
10.1006/jdeq.1999.3683
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发表时间：
2000-03
影响因子：
2.4
通讯作者：
Yi A. Li;P. Olver
中科院分区：
文献类型：
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作者：
Yi A. Li;P. Olver
摘要我们在Sobolev空间Hs中建立了一个可积的非线性色散波动方程的局部适定性，该方程作为浅水波的模型，被称为Camassa-Holm方程。然而，不像更熟悉的Korteweg-deVries模型，我们证明了条件的初始数据，导致有限时间爆破的某些解决方案。
Abstract We establish local well-posedness in the Sobolev space Hs with any s> 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa–Holm equation. However, unlike the more familiar Korteweg–deVries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions.