Infinite energy solutions for the Navier-Stokes equations in R^2

The so-called damped Navier-Stokes equations in the whole 2D space will be considered. The global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly-local spaces will be discussed. In addition, the applications of the developed theory to the classical Navier-Stokes problem in R2 will be also presented.