Related papers: Kolmogorov equations associated to the stochastic …
We show well-posedness for McKean--Vlasov equations with rough common noise and progressively measurable coefficients. Our results are valid under natural regularity assumptions on the coefficients, in agreement with the respective…
The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier-Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be…
We consider the problem of loss and propagation of regularity of transport equation with Osgood vector field. As an application, we obtain a quantitative stability estimate for 2D incompressible Euler equation with generalized Yudovich…
This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove pathwise global existence, uniqueness, and temporal…
The celebrated H\"{o}rmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
We consider incompressible generalized Newtonian fluids in two space dimensions perturbed by an additive Gaussian noise. The velocity field of such a fluid obeys a stochastic partial differential equation with fully nonlinear drift due to…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg--de Vries (KdV) equation on a periodic domain…
We construct H\"older continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can…
This paper focuses on analyzing the error of the randomized Euler algorithm when only noisy information about the coefficients of the underlying stochastic differential equation (SDE) and the driving Wiener process is available. Two classes…
We discretize the stochastic Allen-Cahn equation with additive noise by means of a spectral Galerkin method in space and a tamed version of the exponential Euler method in time. The resulting error bounds are analyzed for the…
This paper is concerned with high moment and pathwise error estimates for both velocity and pressure approximations of the Euler-Maruyama scheme for time discretization and its two fully discrete mixed finite element discretizations. The…
We prove that the implicit time Euler scheme coupled with finite elements space discretization for the 2D Navier-Stokes equations on the torus subject to a random perturbation converges in $L^2(\Omega)$, and describe the rate of convergence…
This paper is concerned with high moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with general additive noise. The implicit Euler-Maruyama scheme and standard…
The time-space fractional cable equation arises from extending the generalized fractional Ohm's law to model anomalous diffusion processes. In this paper, we develop and analyze a numerical approximation for stochastic nonlinear time-space…
We adapt the formalism of the statistical theory of 2D turbulence in the case where the Casimir constraints are replaced by the specification of a prior vorticity distribution. A new relaxation equation is obtained for the evolution of the…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Kolmogorov equation approach.
In this paper, we study the stochastic logrithmic Schr\"odinger equation with saturated nonlinear multiplicative L\'evy noise. The global well-posedness is established for the stochastic logrithmic Schr\"odinger equation in an appropriate…