On the Existence of Long-Time Classical Solutions for the 2D Inviscid Boussinesq Equations - Jiafa Xu; Lishan Liu (Journal of Mathematics)
In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. It is proved that for general initial data u0∈Hs with s>3, the life span of the classical solutions satisfies T>Cln  N3/4.