Remark on the local ill-posedness for KdV equation. (English. Abridged French version) Zbl 0941.35097

Tzvetkov, Nickolay

C. R. Acad. Sci., Paris, Sér. I, Math. 329, No. 12, 1043-1047 (1999).

Summary: We prove that the Cauchy problem for the KdV equation is locally ill-posed in \(\dot H^s\), \(s<-3/4\), if the flow map \(u(0)\mapsto u(t)\) is supposed to be \(C^2\).

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35R25	Ill-posed problems for PDEs

Keywords:

Cauchy problem; KdV equation; locally ill-posed