Energetic Systems and Global Attractors for the 3D Navier-Stokes Equations

The purpose of this paper is to address the question of whether or not there exists a linear space of initial data generating global in time solutions of the initial-boundary value problem for 3-dimensional Navier-Stokes equations (3D NSE), and to establish unconditional results about global attractors for 3D NSE by bypassing the problem of uniqueness and global regularity. For this goal, the author introduces the notion of energetic system which is capable of both incorporating 3D NSE and adequate modelling of properties of 3D NSE