带位势的非聚焦能量临界四阶Schr dinger方程的小初值问题  

Defocusing Energy-critical Fourth-order Schrodinger with Potential and Small Data

作　　者：夏素霞[1] 崔秋月 XIA Suxia;CUI Qiuyue(School of Mathematics and Statistics,Henan University of Technology,Zhengzhou 450001,China)

机构地区：[1]河南工业大学数学与统计学院,河南郑州450001

出　　处：《洛阳理工学院学报(自然科学版)》2025年第1期88-92,共5页Journal of Luoyang Institute of Science and Technology:Natural Science Edition

摘　　要：主要研究一类带位势项的能量临界非聚焦型四阶Schr dinger方程在空间维数n=8时的初值问题。借助带位势项的Strichartz型估计和处理能量临界非线性四阶Schr dinger方程的方法,利用压缩不动点定理证明问题在小初值情形下的局部适定性,结合方程自身满足的守恒律,建立了问题在小初值条件下的整体适定性,并得到了整体解在能量空间中的散射理论。This paper studies the initial value problem for the defocusing energy-critical fourth-order nonlinear Schrodinger equation with potential in space dimension n=8.First,it resorts to the Strichartz type estimates and fourth-order Schrodinger equation with potential and deals with energy-critical nonlinear fourth-order Schrodinger equation.The local well-posedness of the problem for small initial data is established via the contraction mapping principle.By employing the property of conservatism,the global well-posedness of the equations for small initial data is established,as well as the scattering theory of the global solution in the energy space.

关 键 词：四阶Schr dinger方程 位势 适定性 能量临界 散射 

分 类 号：O175.29[理学—数学]