A note on well-posedness for Camassa-Holm equation

By Raphaël Danchin. 2003

297 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a3052cd92184fb8f28f2187e1e531914ac4977af

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In Applied Mathematics

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Citations in the corpus

Local-in-Space Criteria for Blowup in Shallow Water and Dispersive Rod Equations (2012, unknown): “[9] R.”
WELL-POSEDNESS OF HIGHER-ORDER CAMASSA-HOLM EQUATIONS (2009, background): “More relevant for the present paper, we recall that existence and uniqueness results for global weak solutions of (1.3) are proved in [11, 13, 29, 30, 15, 16 ], see also [5].”
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.”
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.”
WELLPOSEDNESS FOR A PARABOLIC-ELLIPTIC SYSTEM (2005, unknown): “We refer to [5, 7, 14, 15] and references therein for more complete information.”
On the well-posedness of the Degasperis-Procesi equation (2006, background): “Existence and uniqueness results for global weak solutions of the Camassa–Holm equation are proved in [4,9,12,34,35,15,16].”
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, background): “(c) Following the proof of Proposition 4 in [17], one can see that (1.”
The Cauchy problem for the integrable Novikov equation (2012, methodology): “The Littlewood–Paley decomposition and nonhomogeneous Besov spaces which were introduced in [16,3] have been used to establish the well-posedness of the Euler equations and the Navier–Stokes equations as well as the Camassa–Holm equation [2–7].”
Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, unknown): “(See [15].”
Low-Regularity Solutions of the Periodic Camassa–Holm Equation (2007, background): “[6], [8], [10], [11], [14], [18], [30] and references therein) and that the soliton solutions do not evolve in C1 - they are peaked solutions with a corner at their crests and referred to as peakons.”
A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation (2006, background): “Danchin, R. (2001).”