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arXiv · 1601.03889

Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing

Shihui Zhu
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Abstract

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 $H^1(\mathbb{R})$.

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Shihui Zhu. 2016-01-15. Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing. https://arxiv.org/abs/1601.03889

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