Strichartz inequalities with white noise potential on compact surfaces

TL;DR

This paper establishes Strichartz inequalities for Schrödinger and wave equations with white noise potential on compact surfaces, using advanced calculus to handle low regularity solutions.

Contribution

It introduces a novel approach to prove Strichartz inequalities with multiplicative noise on 2D manifolds, leveraging the Anderson Hamiltonian and paracontrolled calculus.

Findings

Proves Strichartz inequalities with white noise potential on compact surfaces.

Develops a low regularity solution theory for nonlinear equations with noise.

Utilizes high order paracontrolled calculus for analysis.

Abstract

We prove Strichatz inequalities for the Schr{\"o}dinger equation and the wave equation with multiplicative noise on a two-dimensional manifold. This relies on the Anderson Hamiltonian H described using high order paracontrolled calculus. As an application, it gives a low regularity solution theory for the associated nonlinear equations.