Volume 20, Issue 3
The Dissipative Quasi-geostrophic Equation in Spaces Admitting Singular Solutions

Baoquan Yuan & Jia Yuan

J. Part. Diff. Eq., 20 (2007), pp. 203-219.

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  • Abstract

This paper studies the Cauchy problem of the dissipative quasi-geostrophic equation in pseudomeasure space PM^{n+1-2α}(\mathbb{R}^n) or Lorentz space L\frac{n}{2α-1, ∞}(\mathbb{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.

  • AMS Subject Headings

35Q35, 76U05, 86A05.

Published online: 2007-08