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Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing

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  • 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 $H^1(\mathbb{R})$.
    Mathematics Subject Classification: Primary: 35L05, 35D30; Secondary: 76B15.

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