Smoothing effect for the regularized Schr\"odinger equation with non   controlled orbits
  We prove that the geometric control condition is not necessary to obtain the smoothing effect and the uniform stabilization for the strongly dissipative Schr\"odinger equation. 
Lassaad Aloui (LAMSIN), Moez Khenissi, Georgi Vodev (LMJL)
math.AP