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 ℒp space is the null solution, infinitely many self-similar solutions do exist in weak- ℒp 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. © Springer-Verlag 2007.
Original language | English |
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Pages (from-to) | 111-142 |
Journal | Monatshefte fur Mathematik |
Volume | 151 |
DOIs | |
Publication status | Published - 1 Jun 2007 |
Keywords
- Long time asymptotics
- Quasi-geostrophic equation
- Self-similar solutions