Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
Katrin Grunert, Helge Holden, Xavier Raynaud
TL;DR
This paper proves the existence of global weak dissipative solutions for the two-component Camassa-Holm system with nonvanishing asymptotics, analyzing the effects of the second component on solution regularity and wave breaking.
Contribution
It introduces a framework for global weak dissipative solutions of the 2CH system with nonvanishing asymptotics, exploring the interplay between dissipative and conservative solutions.
Findings
Existence of global weak dissipative solutions for 2CH system.
Analysis of the second component's influence on regularity and wave breaking.
Comparison between dissipative and conservative solution behaviors.
Abstract
We show existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second component in the 2CH system on the regularity of the solution, and, in particular, the consequences for wave breaking, is discussed. Furthermore, the interplay between dissipative and conservative solutions is treated.
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