Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 72, pp. 1-14.

Title: Blow-up criterion for two-dimensional heat
       convection equations with zero heat conductivity

Authors: Yu-Zhu Wang  (North China Univ., Zhengzhou, China)
         Zhiqiang Wei (North China Univ., Zhengzhou, China)

Abstract:
 In this article we obtain a blow-up criterion of smooth solutions
 to Cauchy problem for  the incompressible  heat convection equations
 with  zero  heat conductivity in $\mathbb{R}^2$.
 Our proof is based on careful H\"oder estimates of heat and transport
 equations and the standard Littlewood-Paley theory.
 
Submitted February 28, 2012. Published May 10, 2012.
Math Subject Classifications: 76D03, 35Q35.
Key Words: Heat convection equations; smooth solutions; 
           blow-up criterion.