Abstract
ABSTRACT In this paper, we investigate the generic regularity of global-in-time conservative solutions for the modified coupled Camassa–Holm (CH) system on real line. It has been shown that the modified coupled CH system possible development of singularities in finite time and beyond the occurrence of wave breaking the global conservative solution is existent. In this paper, we further prove that the Cauchy problem of the modified coupled CH system with the initial data has a unique global conservative weak solution. We also study the stability for the unique global conservative solutions. Therefore, we obtain the generic regularity of the conservative weak solutions.
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