Discrete data assimilation via Ladyzhenskaya squeezing property in the 3D viscous primitive equations

We discuss the discrete data assimilation problem for the 3D viscous primitive equations arising in the modeling of large scale phenomena in oceanic dynamics. Our main result states possibility of asymptotically reliable prognosis based on a discrete sequence of finite number of scalar observations. Our method is quite general and can be applied to a wide class of dissipative systems.