Related papers: Stochastic logarithmic Schrodinger equations: ener…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…
Understanding the properties of the stochastic phase field models is crucial to model processes in several practical applications, such as soft matters and phase separation in random environments. To describe such random evolution, this…
By employing a suitable multiplicative It\^o noise with radial structure and with more than linear growth, we show the existence of a unique, global-in-time, strong solution for the stochastic Euler equations in two and three dimensions.…
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized…
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 general integer powers in both the energy and strong regime…
In this article, we consider the stochastic wave equation on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally…
We study a quite general class of stochastic dispersive equations with linear multiplicative noise, including especially the Schr\"odinger and Airy equations. The pathwise Strichartz and local smoothing estimates are derived here in both…
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic…
We study the stochastic Burgers equation driven by an additive Hermite sheet of order $q \ge 1$. The equation is formulated in the mild sense using the heat semigroup, and existence and uniqueness of solutions are established via a…
The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its…
We study the stochastic complex Ginzburg-Landau equation (SCGL) with an additive space-time white noise forcing on the two-dimensional torus. This equation is singular and thus we need to renormalize the nonlinearity in order to give proper…
We consider the stochastic nonlinear Schroedinger equation driven by a multiplicative noise in a semiclassical regime, where the Plank constant is small. In this regime, the solution of the equation exhibits high-frequency oscillations. We…
The stochastic convective Brinkman-Forchheimer (SCBF) equations in an open connected set $\mathcal{O}\subseteq\mathbb{R}^d$ ($d\in \{2,3,4\}$) or torus are considered in this work. We show the existence of a pathwise unique strong solution…
We study the stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on the unit sphere $\mathbb{S}^{2}$. The existence and uniqueness of its solution in certain Sobolev space is investigated and sample…
We consider the cubic Nonlinear Schroedinger Equation (NLS) in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time Hs bounds in terms of the Hs size of the initial data for s >=-1/4…
This article deals with stochastic partial differential equations with quadratic nonlinearities perturbed by small additive and multiplicative noise. We present the approximate solution of the original equation via the amplitude equation…
We address the Cauchy problem for a nonlinear Schr{\"o}dinger equation where the dispersion is modulated by a deterministic noise. The noise is understood as the derivative of a self-affine function of order H $\in$ (0, 1). Due to the…
We consider a stochastic nonlinear defocusing Schr\"{o}dinger equation with zero-order linear damping, where the stochastic forcing term is given by a combination of a linear multiplicative noise in the Stratonovich form and a nonlinear…
We prove a priori bounds for solutions of singular stochastic porous media equations with multiplicative noise in their natural $L^1$-based regularity class. We consider the first singular regime, i.e.~noise of space-time regularity…
In this project we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman-Kac…