A few remarks on the Camassa-Holm equation

By Raphaël Danchin. Differential and Integral Equations, 2001

518 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1d0fbca4f445b85e59e23ff1c79b5d7eda1070b9

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Citations in the corpus

Initial Boundary Value Problems of the Camassa–Holm Equation (2008, background): “(2.6), ũ t x ∈ C 0 T H1 ∩ L 0 T W 1 1 with ũ0 as initial data (Danchin, 2001; Molinet, 2004).”
A Note on the Degasperis-Procesi Equation (2005, background): “2) an initial data with the same regularity will either develop into a wave that exists for all times or wave breaking ocurs [2, 3, 4, 12].”
On the uniqueness in critical spaces for compressible Navier-Stokes equations (2005, background): “Actually, in [8], the proposition below is proved for non-homogeneous Besov spaces (see Proposition A.”
Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation (2006, background): “ D . Holm for useful comments concerning this work.”
Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces (2020, methodology): “1 [18, 19] Assume that (s, p, r) satisfies (1.”
On the well-posedness of the Degasperis-Procesi equation (2006, unknown): “Generalized Degasperis–Procesi equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90”
Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007, background): “Critical Exponent One of the main aims of our article has been to improve the results of Misiolek (2002) and Danchin (2001) so to include the periodic peakons.”
Controllability and asymptotic stabilization of the Camassa–Holm equation (2008, methodology): “5 Remark on the result in Besov spaces In fact it is not more difficult (due do the results already proved in [15] and [31]) and a little more general to establish the above result in the context of Besov spaces.”
Stability of multipeakons (2008, background): “In Section 2 we state a well-posedness result for (C-H) established in [8] and [11].”
Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces (2012, background): “See, for example, [10], [11] (see also [12] for the periodic case), where the well-posedness is also established in slightly rougher spaces of Besov type.”
On the Well-Posedness Problem and the Scattering Problem for the Dullin-Gottwald-Holm Equation (2005, background): “And in [21, 22 ], A. Constantin, J. Escher and R. Danchin studied wave breaking for nonlinear nonlocal shallow water equations, where wave breaking holds if the solution (representing the wave) remains bounded but its slope becomes infinite in finite time.”