带Hartree型非线性项双调和薛定谔方程解的整体适定性  

The Global Well-posedness for the Biharmonic Schrödinger Equations with Hartree Nonlinearity

作　　者：王雪雯 郭青[1] WANG Xuewen;GUO Qing(College of Sciences,Minzu University of China,Beijing 100081)

机构地区：[1]中央民族大学理学院,北京100081

出　　处：《四川师范大学学报（自然科学版）》2021年第6期772-778,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11771469)。

摘　　要：主要研究带Hartree型非线性项的聚焦型双调和Schrödinger方程在质量超临界能量次临界条件下解的整体适定性.运用H2中有界序列的Profile分解得到卷积型Gagliardo-Nirenberg不等式的最佳常数,由此证明双调和Schrödinger方程解的整体适定性.In this paper,we study the global well-posedness for the focusing mass-supercritical and energy-subcritical biharmonic Schrödinger equation. The optimal constant of the convolution Gagliardo-Nirenberg inequality is obtained by using the Profile decomposition of bounded sequence in H^(2),and then the global well-posedness for the biharmonic Schrödinger equations is proved.

关 键 词：聚焦型 双调和Schrödinger方程 质量超临界能量次临界 整体适定性 

分 类 号：O175.29[理学—数学]