Related papers: Exponential Mixing for 3D Stochastic Primitive Equ…

This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation…

The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, H\"older in space, and…

Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak…

We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential stability in the dual-Lipschitz metric holds under the…

We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…

An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…

We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…

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 work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…

In this paper, we establish the exponential mixing property of stochastic models for the incompressible second grade fluid. The general criterion established by Cyril Odasso plays an important role.

We consider suitable weak solutions of 2-dimensional Euler equations on bounded domains, and show that the class of completely random measures is infinitesimally invariant for the dynamics. Space regularity of samples of these random fields…

For an SDE driven by a rotationally invariant $\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\alpha+\gamma>1$, where $\gamma$ denotes the Holder index of the drift coefficient. We prove existence…

Geophysicists have studied 3D Quasi-Geostrophic systems extensively. These systems describe stratified flows in the atmosphere on a large time scale and are widely used for forecasting atmospheric circulation. They couple an inviscid…

In this paper we prove the existence of weak martingale solutions to the stochastic Navier-Stokes Equations driven by pure jump L\'evy processes. Our proof consists of two parts. In the first one, mostly classical, we recall a priori…

This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in time and correlated in space. The stochastic Cahn-Hilliard…

In this paper, we present new types of exponential integrators for Stochastic Differential Equations (SDEs) that take the advantage of the exact solution of (generalised) geometric Brownian motion. We examine both Euler and Milstein…

We consider the numerical approximation of linear damped wave systems by Galerkin approximations in space and appropriate time-stepping schemes. Based on a dissipation estimate for a modified energy, we prove exponential decay of the…

We resolve the issue of uniqueness of weak solutions for linear, inertial fluid-poroelastic-structure coupled dynamics. The model comprises a 3D Biot poroelastic system coupled to a 3D incompressible Stokes flow via a 2D interface, where…

We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity $\nu$, and grows like…

We study the Cauchy problem for a semilinear stochastic Maxwell equation with Kerr-type nonlinearity and a retarded material law. We show existence and uniqueness of strong solutions using a refined Faedo-Galerkin method and spectral…