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Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalised viscosity: a numerical study
| 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
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Submitter: 数学紀要登録作業用
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