Critical Points of Strichartz Functional
Critical Points of Strichartz Functional
复制标题
Strichartz 泛函的关键点
DOI：
10.1080/10586458.2018.1537865
复制
发表时间：
2017
影响因子：
0.5
通讯作者：
V. Zharnitsky
中科院分区：
文献类型：
--
作者：
C. E. Wayne;V. Zharnitsky
摘要研究了一对无限维动力系统，这些系统与Schrödinger方程的Strichartz不等式的最小化/最大化函数的研究自然地联系在一起。一个系统是梯度型，另一个系统是哈密顿系统。研究了这两种系统的临界点集合及其稳定性，以及两者之间的关系。通过数值方法和解析方法的结合，我们论证了高斯函数在一维、二维和三维的一类Strichartz不等式中是一个最大化器。论证简化为对一个涉及二项式系数的明显新的组合不等式的验证。
Abstract We study a pair of infinite dimensional dynamical systems naturally associated with the study of minimizing/maximizing functions for the Strichartz inequalities for the Schrödinger equation. One system is of gradient type and the other one is a Hamiltonian system. For both systems, the corresponding sets of critical points, their stability, and the relation between the two are investigated. By a combination of numerical and analytical methods we argue that the Gaussian is a maximizer in a class of Strichartz inequalities for dimensions one, two, and three. The argument reduces to verification of an apparently new combinatorial inequality involving binomial coefficients.