Identification of the source term in Navier-Stokes system with incomplete data

Abstract

The aim of this work is to get instantaneous information at fixed instant T on pollution term in Navier-Stokes system in which the initial condition is incomplete. The best method which can solve this problem is the sentinel method; It allows estimating the pollution term at which we look for information independently of the missing term that we do not want to identify. So, we prove the existence of such instantaneous sentinel by solving a problem of controllability with constraint on the control.