The Dissipative Quasi-geostrophic Equation in Spaces Admitting Singular Solutions

The Dissipative Quasi-geostrophic Equation in Spaces Admitting Singular Solutions

Year:    2007

Journal of Partial Differential Equations, Vol. 20 (2007), Iss. 3 : pp. 203–219

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2007-JPDE-5303

Journal of Partial Differential Equations, Vol. 20 (2007), Iss. 3 : pp. 203–219

Published online:    2007-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Dissipative quasi-geostrophic equation