open access

https://hdl.handle.net/2115/44437

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

英語

2010-12

IOP Publishing

Nonlinearity

23(12)

3029-3051

We study numerically the long-time evolution of the surface quasi-geostrophic equation with generalized viscosity of the form (-Δ)α, where global regularity has been proved mathematically for the subcritical parameter range α ≥ 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 α = 1/2 is of technical nature.

学術雑誌論文

Accepted Manuscript

This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at 10.1088/0951-7715/23/12/003

0951-7715