(untitled) (Journal of Partial Differential Equations, 2007)
This paper studies the Cauchy problem of the dissipative quasi-geostrophic equation in pseudomeasure space PM^n+1-2α(R^n) or Lorentz space Ln2α-1, ∞(R^n), which admit the singular solutions. The global well-posedness is established provided initial data θ_0(x) are small enough in these spaces. Moreover, the asymptotic stability of solutions in pseudomeasure space is proved. In particular, if the initial data are homo-geneous functions of degree 1 - 2α, the self-similar solutions are also obtained.