On the Cauchy Problem of the Camassa-Holm Equation

By Hui-hui Dai, Kwek Keng-Huat, Hongjun Gao, Chaochun Qu. 2006

200 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/d2c1d2c6fda116e15bcc9cb872e5f18f2ffa8841

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation (2006, unknown): “Local well-posedness results are proved in [9, 20, 33, 38].”
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].”
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.”
Non-Uniform Dependence for the Periodic CH Equation (2010, methodology): “[26] Rodriguez-Blanco, G. (2001).”
Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation (2006, background): “valid for any t R T 0 k@xu(t)k1dt were finite then the solution u could be extended beyond time T . The corollary follows.”
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, background): “For the well-posedness of CH for s > 3/2, we refer the reader to [41], [22], [51] and [63].”
Initial Boundary Value Problems of the Camassa–Holm Equation (2008, methodology): “Applying the local well-posedness result of the periodic Camassa–Holm equation (Constantin and Escher, 1998c; Rodriguez-Blanco, 2001), we have that”
On the well-posedness of the Degasperis-Procesi equation (2006, unknown): “Local well-posedness results are proved in [7, 19, 24, 29].”
Local well‐posedness and blow‐up criteria of solutions for a rod equation (2005, background): “Local well-posedness for the initial datum u0(x) ∈ H with s > 3/2 was proved by several authors, see [14, 16, 18].”
WELL-POSEDNESS OF HIGHER-ORDER CAMASSA-HOLM EQUATIONS (2009, unknown): “Local well-posedness results are proved in [10, 22, 25, 27].”
Global weak solutions for a two-component Camassa–Holm shallow water system (2011, background): “It has been shown that this equation is locally well-posed [13,14,26,41,44] for initial data u0 ∈ H(R), s > (3)2 .”
On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey (2004, result): “This result was improved to s > 3/2 by Li and Olver [24] and Rodriguez-Blanco [27].”
Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces (2020, background): “Concerning the local well-posedness and ill-posedness for the Cauchy problem of the CH equation in Sobolev spaces and Besov spaces, we refer to [10, 11, 18, 19, 22, 25, 28, 30] and the references therein.”