A simple energy pump for the surface quasi-geostrophic equation

We consider the question of growth of high order Sobolev norms of solutions of the conservative surface quasi-geostrophic equation. We show that if s > 0 is large then for every given A there exists initial data with a norm that is small in H^s such that the H^s norm of corresponding solution at some time exceeds A. The idea of the construction is quasilinear. We use a small perturbation of a stable shear flow. The shear flow can be shown to create small scales in the perturbation part of the flow. The control is lost once the nonlinear effects become too large. © Springer-Verlag Berlin Heidelberg 2012.

Duke Scholars

Author Alexander A. Kiselev Mathematics