摘要
This paper studies the Cauchy problem of the dissipative quasi-geostrophic equation in pseudomeasure space PM^n＋1-2α（R^n） or Lorentz space L n/2α-1,∞（R^n）, which admit the singular solutions. The global well-posedness is established provided initial data θ0（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.
基金
B. Yuan was partially supported by the China postdoctoral Science Foundation （No. 20060390530）, Natural Science Foundation of Henan Province （No. 0611055500）, Science Foundation of the Education Department of Henan Province （200510460008） and Doctor Foundation of Henan Polytechnic University.
