Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equations
نویسندگان
چکیده
We analyse the well-posedness of the initial value problem for the dissipative quasigeostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. We prove that the only small self-similar solution in the strong Lp space is the null solution while infinitely many self-similar solutions do exist in weak-Lp spaces and in a recently introduced [6] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterium of self-similarity persistence at large times is obtained.
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