Blow-up criterion for the density dependent inviscid Boussinesq equations

Li Li 1 and Yanping Zhou 2*

Abstract

In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in R N (N ≥ 2). By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq equations. Our result extends the known blow-up criteria.

Keywords: Inviscid Boussinesq equations; Density-dependent; Local existence;Blow-up criterion