Hokkaido University | Library | HUSCAP Advanced Search 言語 日本語 English

# Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalised viscosity: a numerical study

Files in This Item:
 pre959.pdf 4.2 MB PDF View/Open
 Title: Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalised viscosity: a numerical study Authors: Ohkitani, Koji Browse this author Sakajo, Takashi Browse this author Issue Date: 1-May-2010 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 959 Start Page: [1] Abstract: We study numerically the long-time evolution of the surface quasi-geostrophic equation with generalised viscosity of the form $(-¥Delta)^¥alpha$, where global regularity has been proved mathematically for the subcritical parameter range $¥alpha ¥geq ¥frac{1}{2}$. Even in the supercritical range, we have found numerically that smooth evolution persists, but with a very slow and oscillatory damping in the long run. A subtle balance between nonlinear and dissipative terms is observed therein. Notably, qualitative behaviours of the analytic properties of the solution do not change in the super and subcritical ranges, suggesting the current theoretical boundary $¥alpha =¥frac{1}{2}$ is of technical nature. Type: bulletin (article) URI: http://hdl.handle.net/2115/69766 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics