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

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.

Keywords

• Heat convection equations
• smooth solutions
• blow-up criterion