Norm-inflation for periodic NLS equations in negative Sobolev spaces

Rémi Carles (1) , Thomas Kappeler (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Institut für Mathematik [Zürich]

In this paper we consider Schrödinger equations with nonlinearities of odd order 2σ + 1 on T^d. We prove that for σd≥2, they are strongly illposed in the Sobolev space H^s for any s < 0, exhibiting norm-inflation with infinite loss of regularity. In the case of the one-dimensional cubic nonlinear Schrödinger equation and its renormalized version we prove such a result for H^s with s < −2/3.

Domaines: Equations aux dérivées partielles [math.AP]

Rémi Carles, Thomas Kappeler. Norm-inflation for periodic NLS equations in negative Sobolev spaces. Bulletin de la société mathématique de France, 2017, 145 (4), pp.623-642. ⟨10.24033/bsmf.2749⟩. ⟨hal-01176513⟩