具位势项的非齐次四阶Schrödinger方程的适定性研究

doi:10.13371/j.cnki.chin.q.j.m.2026.01.007

数学季刊 ›› 2026, Vol. 41 ›› Issue (1): 82-91.doi: 10.13371/j.cnki.chin.q.j.m.2026.01.007

具位势项的非齐次四阶Schrödinger方程的适定性研究

School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China

收稿日期:2025-08-11 出版日期:2026-03-30 发布日期:2026-03-30
作者简介:XIA Su-xia (1982-), female, native of Puyang, Henan, associate professor of Henan University of Technology, engages in partial differential equation; LI Shuo (2001-), female, native of Zhoukou, Henan, postgraduate student of Henan University of Technology, engages in partial differential equation.
基金资助:
Supported by National Natural Science Foundation of China (Grant No. 11601122).

Global Well-Posedness for the Inhomogeneous Fourth-Order Schrödinger Equation with Potential

School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China

Received:2025-08-11 Online:2026-03-30 Published:2026-03-30
About author:XIA Su-xia (1982-), female, native of Puyang, Henan, associate professor of Henan University of Technology, engages in partial differential equation; LI Shuo (2001-), female, native of Zhoukou, Henan, postgraduate student of Henan University of Technology, engages in partial differential equation.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 11601122).

摘要/Abstract

摘要： The paper considers the initial value problem of inhomogeneous fourth-order Schrödinger equation with potential in energy space H²(R^d). The global well-posedness is obtained in dimensions d≥5 resorting to contractive mapping principle, Strichartz estimates, Caffarelli-Kohn-Nirenberg-type inequality and the continuity method.

关键词: Well-posedness, Inhomogeneous fourth-order Schr?dinger equation, Potential, Strichartz estimates, Continuity method

Abstract: The paper considers the initial value problem of inhomogeneous fourth-order Schrödinger equation with potential in energy space H²(R^d). The global well-posedness is obtained in dimensions d≥5 resorting to contractive mapping principle, Strichartz estimates, Caffarelli-Kohn-Nirenberg-type inequality and the continuity method.

Key words: Well-posedness, Inhomogeneous fourth-order Schr?dinger equation, Potential; Strichartz estimates, Continuity method

中图分类号:

O175.2

夏素霞, 李烁. 具位势项的非齐次四阶Schrödinger方程的适定性研究[J]. 数学季刊, 2026, 41(1): 82-91.

XIA Su-xia, LI Shuo. Global Well-Posedness for the Inhomogeneous Fourth-Order Schrödinger Equation with Potential[J]. Chinese Quarterly Journal of Mathematics, 2026, 41(1): 82-91.

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具位势项的非齐次四阶Schrödinger方程的适定性研究

Global Well-Posedness for the Inhomogeneous Fourth-Order Schrödinger Equation with Potential

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