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

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

arXiv admin note: text overlap with arXiv:1401.0312, arXiv:1509.08569 by other authors

References in corpus (3)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Stability of multipeakons
• Unique Conservative Solutions to a Variational Wave Equation