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New numerical results for the surface quasi-geostrophic equation. (English) Zbl 1238.86001

Summary: 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 P. Constantin, A. J. Majda and E. Tabak [Nonlinearity 7, No. 6, 1495–1553 (1994; Zbl 0809.35057)]. 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.

MSC:

86A10 Meteorology and atmospheric physics
76M22 Spectral methods applied to problems in fluid mechanics

Citations:

Zbl 0809.35057
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References:

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