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

Abstract

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.

Keywords:

• Global existence
• uniqueness
• Newton-Boussinesq system

AMS Subject Classifications:

• 35Q35

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

H. Ma was partially supported by Natural Science Foundation of Hebei Province [grant number F2015201089]. Q. Zhang was partially supported by the National Natural Science Foundation of China [grant number 11501160]; Natural Science Foundation of Hebei Province [grant number A2017201144]; Young Talents Foundation of Hebei Education Department [grant number BJ2017058]; Outstanding Youth Foundation of Hebei University [grant number 2015JQ01]; the Second Batch of Young Talents of Hebei Province. The authors are deeply grateful to the referee and the associated editor for their valuable advice.