On the improved blow-up criterion for the 2D zero diffusivity Boussinesq equations with temperature-dependent viscosity. Issue 12 (10th September 2018)

• Record Type: Journal Article
• Authors: Ye, Zhuan
• Is Part Of: Applicable analysis. Volume 97:Issue 12(2018)
• Page Start: 2037
• Page End: 2058
• Publication Date: 2018-09-10
• Subjects: 2D Boussinesq equations -- variable viscosity -- blow-up criterion; 35Q35 -- 35B65 -- 76D03; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1350849
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: This paper examines the two-dimensional zero diffusivity Boussinesq equations with temperature-dependent viscosity in the whole space. Whether or not its classical solutions global in time existence is a difficult problem and remains open. The main goal of this paper is to establish several blow-up criteria. More precisely, it is proved that is the maximal time interval if and only if the viscosity satisfies or the vorticity satisfies As a direct application of the above results, several other blow-up criteria in the Besov spaces and the multiplier spaces are also established.