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 language | English (US) |
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Journal | Experimental Mathematics |
DOIs | |
State | Accepted/In press - 2018 |
Keywords
- Schroedinger equation
- Strichartz inequality
- extremizers
ASJC Scopus subject areas
- Mathematics(all)