Global regularity results for the 2D Boussinesq equations with partial dissipation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Adhikari, Dhanapati¹  Cao, Chongsheng²  Shang, Haifeng³  Wu, Jiahong⁴  Xu, Xiaojing^5,6  Ye, Zhuan^5,6 

[1] Marywood Univ, Dept Math & Comp Sci, Scranton, PA 18509 USA

[2] Florida Int Univ, Dept Math, Miami, FL 33199 USA

[3] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China

[4] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

[5] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[6] Beijing Normal Univ, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

关键词: Boussinesq equations;    Global regularity;    Partial dissipation;   

DOI  :  10.1016/j.jde.2015.09.049

来源: Elsevier

【 摘 要 】

The two-dimensional (2D) incompressible Boussinesq equations model geophysical fluids and play an important role in the study of the Raleigh Bernard convection. Mathematically this 2D system retains some key features of the 3D Navier-Stokes and Euler equations such as the vortex stretching mechanism. The issue of whether the 2D Boussinesq equations always possess global (in time) classical solutions can be difficult when there is only partial dissipation or no dissipation at all. This paper obtains the global regularity for two partial dissipation cases and proves several global a priori bounds for two other prominent partial dissipation cases. These results take us one step closer to a complete resolution of the global regularity issue for all the partial dissipation cases involving the 2D Boussinesq equations. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free