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Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation

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Abstract.

We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong \({\cal L}^{p}\) space is the null solution, infinitely many self-similar solutions do exist in weak-\({\cal L}^{p}\) spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained.

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Authors and Affiliations

  1. Universitat Autònoma de Barcelona, Spain

    José A. Carrillo

  2. Universidade Federal de Pernambuco, Recife-PE, Brazil

    Lucas C. F. Ferreira

Authors
  1. José A. Carrillo
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  2. Lucas C. F. Ferreira
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Carrillo, J., Ferreira, L. Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation. Mh Math 151, 111–142 (2007). https://doi.org/10.1007/s00605-007-0447-7

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