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

Abstract

AbstractIn this paper we prove the local existence and uniqueness of C1+γ solutions of the Boussinesq equations with initial data υ0, θ0 ∈ C1+γ, ω0, ∇θ0 ∈ Lq for 0 < γ < 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 θ controls the breakdown of C1+γ solutions of the Boussinesq equations.