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New Numerical Results for the Surface Quasi-Geostrophic Equation

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Peter Constantin

  2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, 30010

    Ming-Chih Lai & Yu-Hou Tseng

  3. Department of Mathematics, Georgia Perimeter College, Atlanta, GA, 30338, USA

    Ramjee Sharma

  4. Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, USA

    Jiahong Wu

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  1. Peter Constantin
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  2. Ming-Chih Lai
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  3. Ramjee Sharma
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  4. Yu-Hou Tseng
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  5. Jiahong Wu
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Correspondence to Ramjee Sharma.

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Constantin, P., Lai, MC., Sharma, R. et al. New Numerical Results for the Surface Quasi-Geostrophic Equation. J Sci Comput 50, 1–28 (2012). https://doi.org/10.1007/s10915-011-9471-9

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