10 citations · 17 across the 7 of their papers we have counts for
7 papers
Nonlinear Schrödinger equations with spatial white noise potential on full space for
Antoine Mouzard, Immanuel Zachhuber
In this paper, we prove existence and uniqueness of energy solutions for nonlinear Schrödinger equations with a multiplicative white noise on with . We rely on an expo…
On domains of elliptic operators with distributional coefficients
Immanuel Zachhuber
We show how one can use recently gained insights from the study of singular SPDEs, more particularly the study of singular operators via the theory of Paracontrolled Distributions,…
Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential
Francesco Carlo De Vecchi, Xiaohao Ji, Immanuel Zachhuber
In this paper, we consider the defocusing Hartree NLS with white noise external potential on T^3 i.e. the Hartree NLS whose linear part is given by the Anderson Hamiltonian. A Stri…
Invariant Gibbs measure for Anderson nonlinear wave equation
Nikolay Barashkov, Francesco C. De Vecchi, Immanuel Zachhuber
We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field expl…
Finite speed of propagation for the 2- and 3-dimensional multiplicative stochastic wave equation
Immanuel Zachhuber
We prove finite speed of propagation for the multiplicative stochastic wave equation in two and three dimensions which leads us to a global space-time well-posedness result for the…
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…
Local and global well-posedness of 2d periodic multiplicative stochastic NLS
Immanuel Zachhuber
We use Strichartz estimates with rough potentials like the spatial white noise on the 2 \ dimensional torus to prove global well-posedness of the multiplicative stochastic NLS with…