Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation  

作　　者：DONG BoQing & LIU QingQing School of Mathematical Sciences,Anhui University,Hefei 230039,China 

出　　处：《Science China Mathematics》2010年第10期2733-2748,共16页中国科学：数学（英文版）

基　　金：partially supported by National Natural Science Foundation of China (Grant No.10801001,10771001);Natural Science Foundation of Anhui Education Bureau (Grant No.KJ2008A025);the Innovation Term Fund (Grant No.KJTD002B);the Outstanding Youth Fund (Grant No.KJJQ005) of Anhui University

摘　　要：This paper is concerned with the asymptotic behavior of the two-dimensional dissipative quasigeostrophic equation.Based on the spectral decomposition of the Laplacian operator and iterative techniques,we obtain improved L2 decay rates of weak solutions and derive more explicit upper bounds of higher order derivatives of solutions.We also prove the asymptotic stability of the subcritical quasi-geostrophic equation under large initial and external perturbations.This paper is concerned with the asymptotic behavior of the two-dimensional dissipative quasigeostrophic equation.Based on the spectral decomposition of the Laplacian operator and iterative techniques,we obtain improved L2 decay rates of weak solutions and derive more explicit upper bounds of higher order derivatives of solutions.We also prove the asymptotic stability of the subcritical quasi-geostrophic equation under large initial and external perturbations.

关 键 词：QUASI-GEOSTROPHIC EQUATION L2 DECAY ASYMPTOTIC stability 

分 类 号：O241[理学—计算数学]