能量临界分数阶非线性Schrodinger方程的整体弱解  

Global Weak Solutions for Energy-Critical FractionalNonlinear Schr dinger Equations

作　　者：武少琪 廖梦兰 曹春玲[2] WU Shaoqi;LIAO Menglan;CAO Chunling(School of Mathematics,Hohai University,Nanjing 211100,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]河海大学数学学院,南京211100 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2024年第1期87-91,共5页Journal of Jilin University:Science Edition

基　　金：中央高校基本科研基金(批准号:B230201033;423139);广东省数字信号与图像处理技术重点实验室开放课题基金(批准号:2021GDDSIPL-02);江苏省自然科学基金(批准号:BK20221497)。

摘　　要：利用紧性方法给出能量临界分数阶非线性Schr9dinger方程Cauchy问题解的存在性,并证明Cauchy问题存在整体解.通过构造逼近方程,对满足逼近方程的解序列取极限,得到的极限函数即为能量临界分数阶非线性Schr9dinger方程的整体弱解,并证明该弱解满足能量不等式和质量守恒性质.By using the compactness method,we gaved the existence of solutions to the Cauchy problem of the energy-critical fractio nal nonlinear Schr dinger equation and proved the existence of global solution to the Cauchy problem.By constructing the approximation equation and takin g the limit of the solution sequence satisfying the approximation equation,the obtained limit function was the global weak solution of the energy-critical fractional nonlinear Schr dinger equation,and it was proved that the weak solution satisfied the energy inequality and mass conservation property.

关 键 词：非线性Schr9dinger方程 能量临界 分数阶 弱解 紧性 

分 类 号：O175.2[理学—数学]