  We study the Euler equations with the so-called Ekman damping in the whole 2D
space. The global well-posedness and dissipativity for the weak infinite energy
solutions of this problem in the uniformly local spaces is verified based on
the further development of the weighted energy theory for the Navier-Stokes and
Euler type problems. In addition, the existence of weak locally compact global
attractor is proved and some extra compactness of this attractor is obtained.
