Critical Points of Strichartz Functional

C. Eugene Wayne, Vadim Zharnitsky

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
JournalExperimental Mathematics
DOIs
StateAccepted/In press - Jan 1 2018

Keywords

  • Schroedinger equation
  • Strichartz inequality
  • extremizers

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Critical Points of Strichartz Functional'. Together they form a unique fingerprint.

  • Cite this