In this work we construct a set that attracts a class of solutions of the 3D-Navier-Stokes equations in the weak topology of $L^2(\Omega)$. This set is also weakly compact and, considering this class of solutions, is invariant. We call this set the ``weak global attractor'' for the 3D-Navier-Stokes equations. To construct this set and this specific class of solutions we use the unique global solutions of a collection of ``globally modified Navier-Stokes equations''.
This is a joint work with Alexandre Carvalho (ICMC-USP), Pedro Marín-Rubio (Universidad de Sevilla) e José Valero (Universitas Miguel Hernández).
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