Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing
Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing
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DOI：
10.3934/dcds.2016026
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发表时间：
2016-01
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影响因子：
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通讯作者：
Shihui Zhu
中科院分区：
文献类型：
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作者：
Shihui Zhu
本文用特征线方法研究了具有强迫项的Camassa-Holm(C-H)方程在$H^1(\mathbb{R})中的整体适定性。由于强迫的作用，研究弱解适定性的许多重要性质，如守恒律、可积性等，在没有强迫的情况下是不能从C-H方程继承的。利用平衡律和一些新的估计，我们证明了在$H^1(\mathbb{R})$中具有强迫的C-H方程整体弱解的存在唯一性。
In this paper, we study the global well-posedness for the Camassa-Holm(C-H) equation with a forcing in $H^1(\mathbb{R})$ by the characteristic method. Due to the forcing, many important properties to study the well posedness of weak solutions do not inherit from the C-H equation without a forcing, such as conservation laws, integrability. By exploiting the balance law and some new estimates, we prove the existence and uniqueness of global weak solutions for the C-H equation with a forcing in $H^1(\mathbb{R})$.