Classical solutions of the periodic Camassa—Holm equation

By G. Misiołek. 2002

166 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f5b4c1b2bc3b416339a6c9be4137938d697a44cb

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, background): “Existence and uniqueness results for classical solution of the periodic Camassa–Holm equation was established in [45].”
Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation (2006, methodology): “g strong solution. For further results in this direction we refer to [Mc], [CoE] and the survey article [Mo] and references therein. For well-posedness results in the periodic case we refer to [HM1], [Mi], and [DKT], where the equation is studied in its integral-diﬀerential form (see (1.2) below) as”
Non-Uniform Dependence for the Periodic CH Equation (2010, methodology): “In [23], using energy estimates, it is proved that”
Blow-up of solutions to a nonlinear dispersive rod equation (2006, background): “Local well-posedness for the initial datum u0(x) ∈ H with s > 3/2 was proved by several authors, see [12, 14, 16].”
Blow-up of solutions to the DGH equation (2007, background): “Local well-posedness for the initial datum u0(x) ∈ H with s > 3/2 was proved by several authors, see [26,29,32].”
Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach (2006, result): “In [43] this result was obtained for k ≥ 3/2.”
Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007, background): “[9], [15], [17], [24], [30], [35].”