Critical Points of Strichartz Functional

C. Eugene Wayne, Vadim Zharnitsky

Research output: Contribution to journalArticlepeer-review


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)
Pages (from-to)235-257
Number of pages23
JournalExperimental Mathematics
Issue number2
StatePublished - 2021


  • Schroedinger equation
  • Strichartz inequality
  • extremizers

ASJC Scopus subject areas

  • General Mathematics


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