On the global well-posedness of a generalized 2D Boussinesq equations

In this paper, we consider the global solutions to a generalized 2D Boussinesq equation (Formula Presented), with σ≥0, γ≥0, ν>0, κ>0, α<1 and β<1. When σ=0, γ≥0, α∈[0.95,1) and β∈(1-α,g(α)), where g(α)<1 is an explicit function as a technical bound, we prove that the above equation has a global and unique solution in suitable functional space.