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Strichartz inequalities with white noise potential on compact surfaces

Antoine Mouzard and Immanuel Zachhuber

Vol. 17 (2024), No. 2, 421–454
Abstract

We prove Strichartz inequalities for the Schrödinger equation and the wave equation with multiplicative noise on a two-dimensional manifold. This relies on the Anderson Hamiltonian described using high-order paracontrolled calculus. As an application, it gives a low-regularity solution theory for the associated nonlinear equations.

Keywords
Anderson Hamiltonian, paracontrolled calculus, white noise, Schrödinger operator, Strichartz inequalities
Mathematical Subject Classification
Primary: 35J10, 58J05, 60H25
Milestones
Received: 26 April 2021
Revised: 13 April 2022
Accepted: 15 July 2022
Published: 6 March 2024
Authors
Antoine Mouzard
Université de Rennes, CNRS, IRMAR-UMR 6625
Rennes
France
Immanuel Zachhuber
Freie Universität Berlin
Berlin
Germany

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