半线性SCHRDINGER方程初值问题的L^2-适定性  

L^2-Well-posedness for The Initial-value Problem of A Semilinear Schrdinger Equations

作　　者：阳志锋[1] 邱德华[2] 

机构地区：[1]衡阳师范学院数学与计算科学系,湖南衡阳421008 [2]广东商学院数学与计算科学学院,广东广州510320

出　　处：《数学的实践与认识》2010年第9期180-186,共7页Mathematics in Practice and Theory

基　　金：衡阳师范学院青年项目(08A27)

摘　　要：在R^N(N≥2)中讨论一类具时间依赖系数的半线性Schrdinger方程初值问题的L^2-适定性.在Lorentz空间中,通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了问题的L^2-整体适定性.The L2-well-posedness for the initial-value problem of a semilinear SchrSdinger equations with time-dependent coefficient is studied in RN（N ≥2）. Under Strichartz estimation and priori estimation for the solution in Lorentz space, the relationship between the critical powers a for the well-posedness and the order λ of the zeroes of the coefficient is obtained. And under some conditions, the L2-global well-posedness of the concerned problem is proved.

关 键 词：适定性 半线性Schr5dinger方程 初值问题 STRICHARTZ估计 先验估计 

分 类 号：O175.8[理学—数学]