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	THE TWO-DIMENSIONAL INCOMPRESSIBLE BOUSSINESQ EQUATIONS WITH GENERAL CRITICAL DISSIPATION
	Jiu, Quansen ; Miao, Changxing ; Wu, Jiahong ; Zhang, Zhifei
	2014
关键词	Boussinesq equations critical dissipation global regularity QUASI-GEOSTROPHIC EQUATION GLOBAL WELL-POSEDNESS NAVIER-STOKES EQUATIONS MAXIMUM PRINCIPLE CONVECTION REGULARITY SYSTEM BOUNDS
英文摘要	The two-dimensional incompressible Boussinesq equations with partial or fractional dissipation have recently attracted considerable attention and the global regularity issue has been extensively investigated. This paper aims at the global regularity in the case when the dissipation is critical. The critical dissipation refers to alpha + beta = 1 when Lambda(alpha) = (-Delta)(alpha/2) and Lambda(beta) represent the fractional Laplacian dissipation in the velocity and the temperature equations, respectively. When alpha = 1 and beta = 0 or when alpha = 0 and beta = 1, the global regularity was obtained in [T. Hmidi, S. Keraani, and F. Rousset, J. Differential Equations, 249 (2010), pp. 2147-2174; T. Hmidi, S. Keraani, and F. Rousset, Comm. Partial Differential Equations, 36 (2011), pp. 420-445]. However, the approaches there do not apply to the situation when alpha + beta = 1 with both alpha > 0 and beta > 0. The novelty here is to reduce the critical Boussinesq system to a critical active scalar equation or, more precisely, the generalized critical surface quasi-geostrophic equation. When a is restricted to a suitable range, the global regularity of the critical Boussinesq system can be obtained by exploiting the global regularity of this scalar equation and the global bound for a combined quantity of the vorticity and the temperature.; Mathematics, Applied; SCI(E); EI; 2; ARTICLE; jiuqs@mail.cnu.edu.cn; miao_changxing@iapcm.ac.cn; jiahong@math.okstate.edu; zfzhang@math.pku.edu.cn; 5; 3426-3454; 46
语种	英语
出处	SCI ; EI
出版者	siam journal on mathematical analysis
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/390276]
专题	数学科学学院
推荐引用方式 GB/T 7714	Jiu, Quansen,Miao, Changxing,Wu, Jiahong,et al. THE TWO-DIMENSIONAL INCOMPRESSIBLE BOUSSINESQ EQUATIONS WITH GENERAL CRITICAL DISSIPATION. 2014-01-01.

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