Dispersive equations with invariant measures

2025/09/27 by Nicola Garofalo, Garofalo, Nicola
Mathematics · #22E30 #35C15 #35Q40 #35Q41 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2509.23466

openalex publication_date 2025/09/27 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

In mathematical physics it is of interest to study Schrödinger equations with friction and possessing an invariant measure. The focus of this paper is the Cauchy problem for the Schrödinger equation \p_t f - i \mathscr L f = 0, where \mathscr L = Δ- \sa x,∇\da is the Ornstein-Uhlenbeck operator. We use this as a model to stimulate interest in a new class of possibly degenerate dispersive equations which cannot be treated by the existing theory.

Citations

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Related

• Local Dispersive and Strichartz estimates for the Schrödinger equation associated to the Ornstein-Uhlenbeck operator
• Schrödinger semigroups and the Hörmander hypoellipticity condition
• Dispersive Properties for Discrete Schrodinger Equations
• Nonlinear Schrödinger equation with Ornstein-Uhlenbeck operator
• Dispersive estimates for Schroedinger operators: A survey