A characterization at infinity of bounded vorticity, bounded velocity solutions to the 2D Euler equations (Q2788633)

This article deals with the 2D Euler equations without forcing in the full plane with bounded velocity and vorticity. The aim of this study is to characterize a posteriori all possible behaviors of bounded velocity and vorticity at infinity.NEWLINENEWLINESince the velocity and the vorticity are both bounded, the Biot-Savart law does not hold. Instead, a renormalized Biot-Savart law is introduced in order to characterize the bounded velocity and vorticity for the full plane. Moreover, the properties of the pressure for the full plane are established. The estimates characterizing the behavior of the pressure at infinity are obtained by means of a Riesz transform.