In this work we are interested in the study of controllability andstabilization of the linearized Benjamin-Ono equation withperiodic boundary conditions, which is a generic model forthestudy of weakly nonlinear waves with nonlocal dispersion. It iswell known that theBenjamin-Ono equation has infinite number ofconserved quantities, thus we consider only controls acting in theequation such that the volume of the solution is conserved. Westudy also the stabilization with a feedback law which gives us anexponential decay of the solutions.
