Global existence and uniqueness of Yudovich's solutions to the 3D Newton-Boussinesq system. Issue 10 (27th July 2018)

• Record Type: Journal Article
• Authors: Ma, Hongyan; Zhang, Qian
• Is Part Of: Applicable analysis. Volume 97:Issue 10(2018)
• Page Start: 1814
• Page End: 1827
• Publication Date: 2018-07-27
• Subjects: Global existence -- uniqueness -- Newton-Boussinesq system; 35Q35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1343463
• Languages: English
• ISSNs: 0003-6811

Abstract

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.