A simple energy pump for the surface quasi-geostrophic equation

Details A simple energy pump for the surface quasi-geostrophic equation A simple energy pump for the surface quasi-geostrophic equation

2011-06-22

arxiv.org/abs/1106.4591v1

Mathematics

Analysis of PDEs

5 pages

Scientific paper

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 is exist small in $H^s$ initial data such that the corresponding solution's $H^s$ norm exceeds $A$ at some time. 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.

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