16 citations · 38 across the 43 of their papers we have counts for
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Non-uniform dependence on initial data for the Camassa--Holm equation in Besov spaces: Revisited
Jinlu Li, Yanghai Yu, Weipeng Zhu
In the paper, we revisit the uniform continuity properties of the data-to-solution map of the Camassa--Holm equation on the real-line case. We show that the data-to-solution map of…
Sharp ill-posedness for the generalized Camassa-Holm equation in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation that includes the Camassa-Holm as well as the Novikov equation on the line. We present a new…
Well-posedness and Continuity Properties of the Degasperis-Procesi equation in critical Besov space
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we obtain the local-in-time existence and uniqueness of solution to the Degasperis-Procesi equation in . Moreover, we prove that the data-to-solu…
Non-uniform dependence on initial data for the generalized Camassa-Holm-Novikov equation in Besov space
Xing Wu, Yanghai Yu, Yu Xiao
Considered in this paper is the generalized Camassa-Holm-Novikov equation with high order nonlinearity, which unifies the Camassa-Holm and Novikov equations as special cases. We sh…
Ill-posedness for the Camassa-Holm and related equations in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we give a construction of such that corresponding solution to the Camassa-Holm equation starting from is discontinuous at in th…
Ill-posedness for the Euler equations in Besov spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In the paper, we consider the Cauchy problem to the Euler equations in with . We construct an initial data showing that the correspon…
Ill-posedness for the Burgers equation in Sobolev spaces
Jinlu Li, Yanghai Yu, Weipeng Zhu
In this paper, we considered the Cauchy problem for the Burgers equation and proved that the problem is ill-posed in Sobolev spaces with $s\in[1,\fr32)$.