On the Cauchy problem for the Camassa-Holm equation

By Guillermo Rodriguez-Blanco. 2001

274 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/264b0d2e784fb926743e1972e82d182bc95d9e3c

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In Geometry and Topology

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Citations in the corpus

Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007, result): “(Similar results have also been obtained for the initial value problem on the line—in addition to the aforementioned articles, see in particular Rodriguez-Blanco, 2001 and Xin and Zhong, 2000.)”
Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, background): “It has been shown that the Camassa-Holm equation is locally well-posed [10, 34, 42 ] with the initial data u0 ∈ H s (R), s > 3 . More interestingly, it has global strong solutions [7, 10] and also blow-up solutions in finite time [7, 10, 11, 14, 35] with a different class of initial profiles in the”
Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “It has been shown that this equation is locally well-posed [13,40] for initial data u0 ∈ Hs(S) with s > (3)2 .”
A convergent numerical scheme for the Camassa--Holm equation based on multipeakons (2005, background): “Local and global well-posedness results as well as results concerning breakdown are proved in [8, 12, 16, 17].”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “It has been shown that this equation is locally well-posed [10,33,44] for initial data u0 ∈Hs(R), s > 2 .”
Classical solutions of the periodic Camassa—Holm equation (2002, methodology): “Local wellposedness in the non-periodic case was proved for initial data in H s ( R )”
Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces (2020, unknown): “refer to [10, 11, 18, 19, 22, 25, 28, 30] and the references therein.”
Controllability and asymptotic stabilization of the Camassa–Holm equation (2008, background): “The Camassa-Holm equation has been intensively investigated lately from the point of view of the Cauchy problem, see for instance [2, 4, 5, 6, 7, 15, 16, 17, 22, 23, 24, 27, 33] and references therein.”