Global existence and uniqueness of Yudovich's solutions to the 3D Newton-Boussinesq system

摘要

In this paper, we investigate the global well-posedness for the 3D Newton-Boussinesq equations in a large class of non-decaying vorticity. With the help of the Fourier analysis and the coupling structure, we establish the global-in-time estimate of vorticity in non-Lipschitz vector field. This estimate together with a new observation enables us to obtain the global existence of non-decaying vorticity. More importantly, we show this solution is unique as time develops.