Strichartz inequalities with white noise potential on compact surfaces

Abstract

We prove Strichatz inequalities for the Schr{ö}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.

References in corpus (6)

• Random data Cauchy theory for supercritical wave equations I: Local theory
• Stochastic quantization of Liouville conformal field theory
• Local and global well-posedness of 2d periodic multiplicative stochastic NLS
• Global dynamics of the $2d$ NLS with white noise potential and generic polynomial nonlinearity
• Quasimode and Strichartz estimates for time-dependent Schrödinger equations with singular potentials
• Two dimensional nonlinear Schrödinger equation with spatial white noise potential and fourth order nonlinearity

Cited by in corpus (1)

• Finite speed of propagation for the 2- and 3-dimensional multiplicative stochastic wave equation