The aim of a Luenberger observer is to reconstruct asymptotically the state of a system, based on partial measurements. This is a crucial tool in control theory, notably in order to stabilize a system by state feedback. Here, we will explain the difficulties that appear if we want to implement a Luenberger observer for the full LWWE on the torus, when the measurement is done on a subinterval of the torus. Then, we will give various remedies, notably, we can reconstruct the low frequencies with an explicit exponential decay rate. This is joint work with Lucas Perrin
