It remains an open question if all classical solutions of the inviscid surface quasigeostrophic (SQG) equation are global in time or not. In this article, this issue is addressed through a geometric approach. This article contains three sections. The first section introduces the SQG equation, and presents existing results along with open problems. The second section presents local uniqueness and existence results of the SQG equations. Finally, the third section presents several geometric criteria under which the solutions of the SQG equation become regular for all time. The relation between the geometry of the level curves and the regularity of the solutions is the central focus of this part.
Published November 15, 2017.
Math Subject Classifications: 35Q35, 35B65, 76B03.
Key Words: Global regularity; quasigeostrophic equations; geometric criteria.
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| Ramjee Sharma |
Department of Mathematics
University of North Georgia
3820 Mundy Mill Rd
Oakwood, GA 30566, USA
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