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arXiv · 1712.07239

Critical points of Strichartz functional

C. Eugene Wayne·Vadim Zharnitsky
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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 Schr\"odinger 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.

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C. Eugene Wayne, Vadim Zharnitsky. 2017-12-19. Critical points of Strichartz functional. https://arxiv.org/abs/1712.07239

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