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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
DOI: 10.2140/apde.2024.17.421
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
© 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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