On Stability and Instability of $$C^{1,\alpha }$$ Singular Solutions to the 3D Euler and 2D Boussinesq Equations

On asymptotic properties of the Boussinesq equations

“…Results on the global existence have been well-established in the presence of the positive thermal diffusivity, namely with −κ∆ρ in the second equation of the Boussinesq system. On the other hand, there has been considerable recent progress in the inviscid case with no diffusivity in the density; see [10][11][12][13]20].…”