GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION

By Alberto Bressan, Adrian Constantin. 2007

558 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b8891729ce9495e7c7ea4bb4bebf767756c42418

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Citations in the corpus

Stability of multipeakons (2008, unknown): “It is worth pointing out that recently, in [3] and [4], Bressan and Constantin have constructed global conservative and dissipative solutions of the Camassa–Holm equation for any initial data in H 1(R).”
Non-Uniform Dependence for the Periodic CH Equation (2010, methodology): “The non-periodic Cauchy problem is also locally well-posed in Hs for s > 3/2 (see Constantin and Escher [4], Li and Olver [19], Rodriguez-Blanco [26], [7], or a survey in Molinet [25]).”
On the Cauchy problem for the two-component Camassa–Holm system (2011, background): “After wave breaking the solutions can be continued uniquely as either global conservative [3] or global dissipative solutions [4].”
Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces (2020, background): “Bressan–Constantin proved the existence of the global conservative solutions [2] and global dissipative solutions [3] in H(1)(R).”
Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, background): “In [3] and [4] the authors show that the solutions can be uniquely continued after breaking as either global conservative of global dissipative weak solution.”
Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, background): “After wave breaking the solutions can be continued as either global conservative or global dissipative solutions [3,4,29].”
Dissipative solutions for the Camassa-Holm equation (2009, methodology): “The procedure in [4] yields a unique semigroup of solutions in H 1 .”
The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation (2010, background): “The sharpest results for the global existence and blow-up solutions are found in Bressan and Constantin [2,3].”
Global weak solutions for a two-component Camassa–Holm shallow water system (2011, background): “On the other hand, it has global weak solutions in H 1(R) [2,3,15,22,47].”
Global Solutions for the Two-Component Camassa–Holm System (2011, background): “for dissipative solutions. Both classes will in general have weak solutions rather than smooth solutions. To identify and characterize the two classes has turned out to be rather involved, see, e.g., [1, 2, 18, 19, 8, 10], and references therein. The approach in this paper characterizes conservative”
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, background): “After wave breaking the solutions of the CH equation can be continued uniquely as either global conservative [2] or global dissipative solutions [3].”