一般幂次散焦导数薛定谔方程解在Hs中的不适定性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1768-1781.

• 论文 • 上一篇

一般幂次散焦导数薛定谔方程解在H^s中的不适定性

陈兴发, 钟澎洪

广东第二师范学院数学学院, 广州 510303

收稿日期:2021-06-23 修回日期:2022-08-06 发布日期:2022-12-16
通讯作者: 钟澎洪,E-mail:zhonghong737@163.com E-mail:zhonghong737@163.com
作者简介:陈兴发,E-mail:zhonghong737@163.com
基金资助:
国家自然科学基金青年基金(11601092)、广东省普通高校重点领域专项(ZDZX1088)和广州市科技计划项目基金(202102080428)

The Ill-Posedness of the Solution for the General Power Derivative Schrödinger Equation in H^s

Chen Xingfa, Zhong Penghong

School of Mathematics, Guangdong University of Education, Guangzhou 510303

Received:2021-06-23 Revised:2022-08-06 Published:2022-12-16
Supported by:
Supported by National Science Foundation for Young Scientists of China(11601092), the Special Projects in Key Fields of Ordinary Colleges and Universities in Guangdong Province(ZDZX1088) and the Fund for Science and Technology of Guangzhou(202102080428)

摘要/Abstract

摘要： 该文研究具有一般幂次散焦非线性导数薛定谔方程,给出了解的构造并证明该解在索伯列夫空间H^s中是不适定的.当$2\leq k\leq4$时,解在H^s中不适定指标$s$的上界为$1/k$;当$k>4$时,不适定指标$s$的上界为$1/2-1/k$.

关键词: 不适定性, 导数薛定谔方程, 正则性

Abstract: The nonlinear defocusing Schrödinger equations with general power nonlinearity are proved to be ill-posed in the Sobolev space H^s whenever the exponent $s$ is lower than $1/k$ ($2 \leq k \leq 4$) or $1/2-1/k$ ($k>4$).

Key words: Ill-posedness, DNLS-type equations, Regularity

中图分类号:

O175.29

陈兴发, 钟澎洪. 一般幂次散焦导数薛定谔方程解在H^s中的不适定性[J]. 数学物理学报, 2022, 42(6): 1768-1781.

Chen Xingfa, Zhong Penghong. The Ill-Posedness of the Solution for the General Power Derivative Schrödinger Equation in H^s[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1768-1781.

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一般幂次散焦导数薛定谔方程解在H^s中的不适定性

The Ill-Posedness of the Solution for the General Power Derivative Schrödinger Equation in H^s

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一般幂次散焦导数薛定谔方程解在Hs中的不适定性

The Ill-Posedness of the Solution for the General Power Derivative Schrödinger Equation in Hs

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一般幂次散焦导数薛定谔方程解在H^s中的不适定性

The Ill-Posedness of the Solution for the General Power Derivative Schrödinger Equation in H^s