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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.

Published online: 2007-08

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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.

  • Keywords

Dissipative quasi-geostrophic equation singular solutions pseudomeasure spaces Lorentz space global well-posedness

  • AMS Subject Headings

35Q35 76U05 86A05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-20-203, author = {Baoquan Yuan and Jia Yuan }, title = {The Dissipative Quasi-geostrophic Equation in Spaces Admitting Singular Solutions}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {3}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5303.html} }
TY - JOUR T1 - The Dissipative Quasi-geostrophic Equation in Spaces Admitting Singular Solutions AU - Baoquan Yuan & Jia Yuan JO - Journal of Partial Differential Equations VL - 3 SP - 203 EP - 219 PY - 2007 DA - 2007/08 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5303.html KW - Dissipative quasi-geostrophic equation KW - singular solutions KW - pseudomeasure spaces KW - Lorentz space KW - global well-posedness AB -

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.

Baoquan Yuan and Jia Yuan . (2007). The Dissipative Quasi-geostrophic Equation in Spaces Admitting Singular Solutions. Journal of Partial Differential Equations. 20 (3). 203-219. doi:
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