Data assimilation for the barotropic Navier-Stokes system

We consider a continuous data assimilation method for the barotropic Navier–Stokes system. The observed solution is supposed to be bounded on the whole time period of observation, while the synchronized solution, usually provided by a numerical method, belongs to the class of dissipative solutions that is considerably larger than the class of conventional weak solutions. A complete synchronization is shown on any compact prediction interval provided the nudging parameters are chosen appropriately.