  Usually, the systems of partial differential equations (PDEs) are discovered
from observational data in the single vector equation form. However, this
approach restricts the application to the real cases, where, for example, the
form of the external forcing is of interest. In the paper, a multi-objective
co-evolution algorithm is described. The single equations within the system and
the system itself are evolved simultaneously to obtain the system. This
approach allows discovering the systems with the form-independent equations. In
contrast to the single vector equation, a component-wise system is more
suitable for expert interpretation and, therefore, for applications. The
example of the two-dimensional Navier-Stokes equation is considered.
