Smoothing effect for the regularized Schrödinger equation with non controlled orbits

Lassaad Aloui (1) , Moez Khenissi (2) , Georgi Vodev (3)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
2 Ecole supérieur de Sciences et Technique de Hammam Sousse
3 LMJL - Laboratoire de Mathématiques Jean Leray

We prove that the geometric control condition is not necessary to obtain the smoothing effect and the uniform stabilization for the strongly dissipative Schrödinger equation.

Mots clés: Geometric Control; Smoothing effect; Resolvent estimates; Stabilization; Geometric Control.

Domaines: Equations aux dérivées partielles [math.AP]

Lassaad Aloui, Moez Khenissi, Georgi Vodev. Smoothing effect for the regularized Schrödinger equation with non controlled orbits. Communications in Partial Differential Equations, 2013, 38 (2), pp.265--275. ⟨hal-00587257v2⟩