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 incremen...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.展开更多
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.
文摘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.
