Related papers: Hyperbolic Anderson model 2: Strichartz estimates …

The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and…

This paper attempts to obtain necessary and sufficient conditions to solve the parabolic Anderson model with fractional Gaussian noises: $\frac{\partial}{\partial t}u(t,x)=\frac{1}{2}\Delta u(t,x)+u(t,x)\dot{W}(t,x)$, where $ {W}(t,x)$ is…

In this note we study the 2d stochastic quasi-geostrophic equation in $\mathbb{T}^2$ for general parameter $\alpha\in (0,1)$ and multiplicative noise. We prove the existence of martingale solutions and pathwise uniqueness under some…

This paper proves Strichartz estimates for the Schrodinger Equation with a potential term and white noise dispersion in dimension $1$. We also explore dispersive estimates using previous results in the field.

The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…

In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on the pattern. As such model we consider an anisotropic Swift-Hohenberg equation adding an additive noise. We prove the…

A metric measure space equipped with a Dirichlet form is called recurrent if its Hausdorff dimension is less than its walk dimension. In bounded domains of such spaces we study the parabolic Anderson models \[ \partial_{t} u(t,x) = \Delta…

In this paper, we aim to prove the existence of global Martingale solution to Stochastic Constrained Modified Swift-Hohenberg Equation driven by stratonovich multiplicative noise. This equation belongs to class of amplitude equations which…

We study the nonlinear stochastic heat equation in the spatial domain $\mathbb {R}$, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on $\mathbb {R}$,…

In this paper, we study the parabolic Anderson model of Skorohod type driven by a fractional Gaussian noise in time with Hurst parameter $H \in (0, 1/2)$. By using the Feynman-Kac representation for the $L^p(\Omega)$ moments of the…

We consider the 2D stochastic Navier-Stokes equations driven by noise that has the regularity of space-time white noise but doesn't exactly coincide with it. We show that, provided that the intensity of the noise is sufficiently weak at…

We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the…

We introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of…

We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…

We propose a $\theta$-scheme to discretize the $d$-dimensional stochastic cubic Schr\"odinger equation in Stratono\-vich sense. A uniform bound for the Hamiltonian of the discrete problem is obtained, which is a crucial property to verify…

In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…

In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential…

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…

A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…

We define the Anderson hamiltonian on the two dimensional torus $\mathbb R^2/\mathbb Z^2$. This operator is formally defined as $\mathscr H:= -\Delta + \xi$ where $\Delta$ is the Laplacian operator and where $\xi$ belongs to a general class…