Journal of Scientific Computing

, Volume 50, Issue 1, pp 1–28

New Numerical Results for the Surface Quasi-Geostrophic Equation

  • Peter Constantin
  • Ming-Chih Lai
  • Ramjee Sharma
  • Yu-Hou Tseng
  • Jiahong Wu
Article

DOI: 10.1007/s10915-011-9471-9

Cite this article as:
Constantin, P., Lai, MC., Sharma, R. et al. J Sci Comput (2012) 50: 1. doi:10.1007/s10915-011-9471-9

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.

Keywords

Global regularity Parallel computation Surface quasi-geostrophic equation 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Peter Constantin
    • 1
  • Ming-Chih Lai
    • 2
  • Ramjee Sharma
    • 3
  • Yu-Hou Tseng
    • 2
  • Jiahong Wu
    • 4
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan
  3. 3.Department of MathematicsGeorgia Perimeter CollegeAtlantaUSA
  4. 4.Department of MathematicsOklahoma State UniversityStillwaterUSA

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