New estimates for the Navier–Stokes equations and globally steady approximations

For the two-dimentional Navier–Stokes equations and a number of their globally steady approximations (Galerkin–Faedo method, discrete in time Galerkin–Faedo method, implicit finite-difference methods ($19_i$)) there obtained new a priori estimates which prove existence of a compact minimal global $B$-attractor for the Navier–Stokes equations (this fact was first proved by the author in 1972, see [1]) as well as for the approximations mentioned. Similar results for many problems of the viscous incompressible fluid theory and continuum mechanics are valid.