Strichartz inequalities with white noise potential on compact surfaces

Antoine Mouzard (1, 2) , Immanuel Zachhuber (3)

1 UR - Université de Rennes
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 FU Berlin - Institut für Mathematik

We prove Strichatz inequalities for the Schrödinger 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.

Keywords: Paracontrolled calculus; Anderson Hamiltonian; White noise; Schrödinger operator; Strichartz inequalities

Domains: Analysis of PDEs [math.AP]; Probability [math.PR]; Spectral Theory [math.SP]; Mathematical Physics [math-ph]

Antoine Mouzard, Immanuel Zachhuber. Strichartz inequalities with white noise potential on compact surfaces. 2021. ⟨hal-03198650v2⟩