THE DISSIPATIVE QUASI-GEOSTROPHIC EQUATION IN SPACES ADMITTING SINGULAR SOLUTIONS

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Dissipative quasi-geostrophic equation singular solutions pseudomeasure spaces Lorentz space global well-posedness
• 年，卷（期）: 2007,（3）
• 页码范围: 203-219
• 页数: 17页
• 分类号: O175.29|O175.26
• 语种: 英文

摘要

This paper studies the Cauchy problem of the dissipative quasi-geostrophic equation in pseudomeasure space PMn+1-2α(Rn) or Lorentz space Ln/2α-1, ∞(Rn), which admit the singular solutions. The global well-posedness is established provided initial dataθ0 (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 homogeneous functions of degree 1-2α, the self-similar solutions are also obtained.