王灯,杨晗.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*[J].数学年刊A辑,2022,43(2):137~152
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 Schr¨odinger Equations with Initial Data in b Lp-Spaces
Received:April 19, 2021  Revised:January 10, 2022
DOI:10.16205/j.cnki.cama.2022.0010
中文关键词:  四阶Schr¨odinger方程, 整体解, Lp初值, Strichartz估计
英文关键词:Fourth-order Schr¨odinger equations, Global solution, b Lp-initial data, Strichartz estimates
基金项目:
Author NameAffiliation
WANG Deng School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China. 
ANG Han School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China. 
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中文摘要:
      本文考虑当初值u0 ∈ Lp 时,四阶非线性Schr¨odinger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Schr¨odinger方程启发,借助一个关于Lp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Schr¨odinger方程的柯西问题的解的整体存在性.
英文摘要:
      The purpose of this paper is to study global well-posedness of the Cauchy problem for the nonlinear fourth-order Schr¨odinger equations with initial data u0 ∈ b Lp. Much less is known about the solvability of this Cauchy problem when p /= 2. Moreover, motivated by some results for the second-order Schr¨odinger equations, and with an data-decomposition lemma for b Lp-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.
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