On the regularity of the flow map associated with the 1D cubic periodic half-wave equation. (English) Zbl 1363.35063

Georgiev, Vladimir; Tzvetkov, Nikolay; Visciglia, Nicola

Differ. Integral Equ. 29, No. 1-2, 183-200 (2016).

Summary: We prove that the solution map associated with the 1D half-wave cubic equation in the periodic setting cannot be uniformly continuous on bounded sets of the periodic Sobolev spaces \(H^s\) with \(s\in (\frac{1}{4}, \frac{1}{2})\).

MSC:

35B65	Smoothness and regularity of solutions to PDEs
35B20	Perturbations in context of PDEs
35B45	A priori estimates in context of PDEs

Keywords:

local well-posedness; ill-posedness; Szegő equation