Global Well-posedness and Global Attractor for Two-dimensional Zakharov-Kuznetsov Equation  

作　　者：Min Jie SHAN 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第9期969-1000,共32页数学学报（英文版）

基　　金：Supported by China Postdoctoral Science Foundation(Grant No.2019M650872);The author would like to express his deep gratitude to Professor Yoshio Tsutsumi,Professor Baoxiang Wang and Professor Liqun Zhang for their guidance and help.

摘　　要：The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in H^s(R^2)for all 5/7<s<1 via using I-method in the context of atomic spaces.By means of the increment of modified energy,the existence of global attractor for the weakly damped,forced Zakharov-Kuznetsov equation is also established in H^s(R^2)for10/11<s<1.

关 键 词：Zakharov-Kuznetsov equation global well-posedness global attractor I-METHOD atomic spaces 

分 类 号：O411.1[理学—理论物理]