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  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.
|Journal||Monatshefte fur Mathematik|
|Publication status||Published - 1 Jun 2007|
- Long time asymptotics
- Quasi-geostrophic equation
- Self-similar solutions