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Journal of Function Spaces
Volume 2014, Article ID 538374, 6 pages
http://dx.doi.org/10.1155/2014/538374
Research Article

Asymptotic Study of the 2D-DQGE Solutions

Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received 29 March 2014; Accepted 7 May 2014; Published 7 July 2014

Academic Editor: Mohamed Abdalla Darwish

Copyright © 2014 Jamel Benameur and Mongi Blel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent . We prove that if the initial data is small enough in the critical space , then the regularity of the solution is of exponential growth type with respect to time and its norm decays exponentially fast. It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces for . Moreover, we give some general properties of the global solutions.