Local existence and blow-up criterion of Holder continuous solutions of the Boussinesq equations

Abstract

In this paper we prove the local existence and uniqueness of C1+gamma solutions of the Boussinesq equations with initial data v(0), theta(0) epsilon C1+gamma, w(0), del theta(0) epsilon L-q for 0 < gamma < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely we show that the gradient of the passive scalar theta controls the breakdown of C1+gamma solutions of the Boussinesq equations.