On the global well-posedness for the 2D Euler-Boussinesq system

This paper is dedicated to the study of the Cauchy problem for the 2D Euler-Boussinesq system. We obtain the global existence of a unique solution for this system without any smallness conditions imposed on the data. In particular, we prove the uniqueness of the system with nondecaying initial vorticity at infinity. Our methods mainly rely upon loss of regularity estimate and Bony's paraproduct.