四阶非线性Schrodinger方程在L^(p)初值空间中解的整体存在性研究  

Existence of Global Solution for the Nonlinear Fourth-Order Schrodinger Equations with Initial Data inL^(p)-Spaces

作　　者：王灯 杨晗[1] WANG Deng;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756

出　　处：《数学年刊（A辑）》2022年第2期137-152,共8页Chinese Annals of Mathematics

摘　　要：本文考虑当初值u0∈L^(p)时,四阶非线性Schrodinger方程的柯西问题的整体适定性.在p≠2的情形下,关于该柯西问题的解的存在性结论较少.受已有二阶Schrodinger方程启发,借助一个关于L^(p)初值的分解引理和Strichartz估计,在p>2且非线性项指数满足一定条件下,本文得到了该四阶非线性Schrodinger方程的柯西问题的解的整体存在性.The purpose of this paper is to study global well-posedness of the Cauchy problem for the nonlinear fourth-order Schrodinger equations with initial data u0∈L^(p).Much less is known about the solvability of this Cauchy problem when p≠2.Moreover,motivated by some results for the second-order Schrodinger equations,and with an data-decomposition lemma forL^(p)-spaces and the Strichartz estimates,the authors show that the problem has a global solution in the case of p>2 and under some conditions of nonlinear term index.

关 键 词：四阶Schrodinger方程 整体解 L^(p)初值 STRICHARTZ估计 

分 类 号：O175.29[理学—数学]