Fronts and pulses near plane Kolmogorov flow. Linear theory

We consider the Kolmogorov problem of viscous incompressible planar fluid flow under external spatially periodic forcing. For the study of time-independent bounded solutions near the instability threshold we use the spatial dynamics formulation. The dynamics is generated by translations in the unbounded spatial direction. The first step of the reduction, i.e. the study of the linear problem was done. Several conserved quantities of the spatial dynamics of the Navier-Stokes system that simplify the study of the nonlinear problem were found.