10 citations · 16 across the 12 of their papers we have counts for
8 papers · 1 filter
Periodic nonlinear Schrödinger equation with distributional potential and invariant measures
Arnaud Debussche, Antoine Mouzard
In this paper, we continue some investigations on the periodic NLSE started by Lebowitz, Rose and Speer and by Bourgain with the addition of a distributional multiplicative potenti…
Anderson stochastic quantization equation
Hugo Eulry, Antoine Mouzard, Tristan Robert
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfac…
A simple construction of the Anderson operator via its quadratic form in dimensions two and three
Antoine Mouzard, El Maati Ouhabaz
We provide a simple construction of the Anderson operator in dimensions two and three. This is done through its quadratic form. We rely on an exponential transform instead of the r…
The logarithmic Schr{ö}dinger equation with spatial white noise on the full space
Quentin Chauleur, Antoine Mouzard
We solve the Schr{ö}dinger equation with logarithmic nonlinearity and multiplicative spatial white noise on R d with d 2. Because of the nonlinearity, the regularity structur…
Scattering, random phase and wave turbulence
Erwan Faou, Antoine Mouzard
We start from the remark that in wave turbulence theory, exemplified by the cubic twodimensional Schr{ö}dinger equation (NLS) on the real plane, the regularity of the resonant mani…
Strichartz inequalities with white noise potential on compact surfaces
Antoine Mouzard, Immanuel Zachhuber
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 Hamiltonia…
Weyl law for the Anderson Hamiltonian on a two-dimensional manifold
Antoine Mouzard
We define the Anderson Hamiltonian H on a two-dimensional manifold using high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We get lower an…
Paracontrolled calculus for quasilinear singular PDEs
I. Bailleul, A. Mouzard
We develop further in this work the high order paracontrolled calculus setting to deal with the analytic part of the study of quasilinear singular PDEs. A number of continuity resu…