Some results on the two-dimensional dissipative Euler equations

Abstract

We make a review of some recent results concerning special solutions and behavior at infinity for 2D dissipative Euler equations. In particular, we give a simplified proof --in the space-periodic setting-- of the uniform space/time boundedness of the first derivatives of the velocity, under suitable assumptions on the external force and on the dissipation (damping) coefficient. This is used to sketch the proof of existence of almost-periodic solutions