Existence and L^2 decay estimate of global strong solution for 2-D incompressible Navier-Stokes equations with logarithmic damping

In this paper, we consider the following Cauchy problem for the 2-D incompressible Navier-Stokes equations with logarithmic damping (1.1). We prove that the existence and uniqueness of global strong solution for the Cauchy problem by applying the classical energy estimates methods. Moreover, we show the the large time behavior of strong solution to the Cauchy problem by means of Fourier splitting method.