1,111 research outputs found
Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation
In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE,
2005) to study the level set dynamics of the 2D quasi-geostrophic equation.
Under certain assumptions on the local geometric regularity of the level sets
of , we obtain global regularity results with improved growth estimate
on . We further perform numerical simulations to
study the local geometric properties of the level sets near the region of
maximum . The numerical results indicate that the
assumptions on the local geometric regularity of the level sets of in
our theorems are satisfied. Therefore these theorems provide a good explanation
of the double exponential growth of observed in this
and past numerical simulations.Comment: 25 pages, 10 figures. Corrected a few typo
- …