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

2016/01/15 by Zhu, Shihui
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.03889

Abstract

In this paper, we study the global well-posedness for the Camassa-Holm(C-H) equation with a forcing in H¹(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 H¹(ℝ).

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