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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 1, 2020, pp. 83–101
DOI: 10.4171/ZAA/1652

Published online: 2020-01-24

Blow-Up Criterion of Strong Solution with Vacuum for the 2D Nonhomogeneous Density-Temperature-Dependent Boussinesq Equations

Zhuan Ye[1]

(1) Jiangsu Normal University, Xuzhou, China

In this paper, we are devoted to the study of the two-dimensional (2D) nonhomogeneous density-temperature-dependent Boussinesq equations with zero diffusivity over bounded domains. We obtain a blow-up criterion in terms of the gradient of viscosity for strong solutions with vacuum. The main ingredient of the proof is the utilization of two logarithmic type inequalities.

Keywords: Nonhomogeneous fluid, blow-up criterion, strong solution, vacuum

Ye Zhuan: Blow-Up Criterion of Strong Solution with Vacuum for the 2D Nonhomogeneous Density-Temperature-Dependent Boussinesq Equations. Z. Anal. Anwend. 39 (2020), 83-101. doi: 10.4171/ZAA/1652