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Existence and decay of solution to the two-dimensional quasigeostrophic equation
TANG Shigan *
College of Mathematics and Statistics, University of Chongqing, Chongqing 401331
*Correspondence author
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Funding: none
Opened online: 8 February 2018
Accepted by: none
Citation: TANG Shigan.Existence and decay of solution to the two-dimensional quasigeostrophic equation[OL]. [ 8 February 2018] http://en.paper.edu.cn/en_releasepaper/content/4743453
In this paper, the authors consider the existence and decay of the global solutions of the quasi-geostrophic equation. In the second part of the paper, the authors firstly consider the existence of the solutions by using the Galerkin approximation method the periodic case in a domain, and then give some energy estimates and employ the compactness theorem in Sobolev space to obtain the existence of the global solutions. In addition, the uniqueness of the solutions can be obtained using the Gronwall inequality. In the third part of the paper, the author use the Fourier splitting method to give decay estimates of the solutions. The decay rate is $(e+t)^{-1
Keywords:quasi-geostrophic equation; decay estimates; Galerkin approximation method; Fourier splitting method.

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