A simple energy pump for the surface quasi-geostrophic equation


Journal Article

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 Hs such that the Hs 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.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A; Nazarov, F

Published Date

  • December 1, 2012

Published In

  • Nonlinear Partial Differential Equations: the Abel Symposium 2010

Start / End Page

  • 175 - 179

Digital Object Identifier (DOI)

  • 10.1007/978-3-642-25361-4_9

Citation Source

  • Scopus