70 citations · 235 across the 17 of their papers we have counts for
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A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa-Holm system
Sondre Tesdal Galtung, Xavier Raynaud
We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa--Holm system (2CH) as the governing equations. Af…
Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system
Katrin Grunert, Xavier Raynaud
Compared with the two-component Camassa-Holm system, the modified two-component Camassa-Holm system introduces a regularized density which makes possible the existence of solutions…
A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system
Katrin Grunert, Helge Holden, Xavier Raynaud
We introduce a novel solution concept, denoted -dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy prob…
Periodic conservative solutions for the two-component Camassa-Holm system
Katrin Grunert, Helge Holden, Xavier Raynaud
We construct a global continuous semigroup of weak periodic conservative solutions to the two-component Camassa-Holm system, an…
Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
Katrin Grunert, Helge Holden, Xavier Raynaud
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 asy…
Global solutions for the two-component Camassa-Holm system
K. Grunert, H. Holden, X. Raynaud
We prove existence of a global conservative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line, allowing for nonvanishing and distinct asymp…