Title: New Numerical Results for the Surface Quasi-Geostrophic Equation
Authors: Constantin, Peter
Lai, Ming-Chih
Sharma, Ramjee
Tseng, Yu-Hou
Wu, Jiahong
Department of Applied Mathematics
Keywords: Global regularity;Parallel computation;Surface quasi-geostrophic equation
Issue Date: 1-Jan-2012
Abstract: The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.
URI: http://dx.doi.org/10.1007/s10915-011-9471-9
ISSN: 0885-7474
DOI: 10.1007/s10915-011-9471-9
Volume: 50
Issue: 1
Begin Page: 1
End Page: 28
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