Ill-posedness of the Camassa–Holm and related equations in the critical space

By Zihua Guo, Xingxing Liu, Luc Molinet, Zhaoyang Yin. Journal of Differential Equations, 2018

133 citations recorded by the source corpus.

Abstract We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space H 3 / 2 and even in the Besov space B p , r 1 + 1 / p for p ∈ [ 1 , ∞ ] , r ∈ ( 1 , ∞ ] . Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ( [5] , [14] , [16] ).

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

View Paper: https://www.semanticscholar.org/paper/c92933a165d243dc16bfd1f184679a9d63906947

Citations in the corpus

• 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.”