相关论文: Regularization by noise for the point vortex model…

We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the…

We consider the generalised Surface Quasi-Geostrophic (gSQG) equations in $\mathbb R^2$ with parameter $\beta\in (0,1)$, an active scalar model interpolating between SQG ($\beta=1$) and the 2D Euler equations ($\beta=0$) in vorticity form.…

Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato (see G. Da Prato and A. Debussche, Ergodicity for the 3D stochastic Navier-Stokes equations, J. Math. Pures Appl., 2003), is reviewed…

Assessing data informativity, determining whether the measured data contains sufficient information for a specific control objective, is a fundamental challenge in data-driven control. In noisy scenarios, existing studies deal with system…

Collapse models postulate the existence of intrinsic noise which modifies quantum mechanics and is responsible for the emergence of macroscopic classicality. Assessing the validity of these models is extremely challenging because it is…

This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

We analyze the influence of noise for qubits implemented using a triple quantum dot spin system. We give a detailed description of the physical realization and develop error models for the dominant external noise sources. We use a Davies…

We investigate enstrophy variations by collapse of point vortices in an inviscid flow and, in particular, focus on the enstrophy dissipation that is a significant property characterizing 2D turbulent flows. Point vortex is an ideal vortex…

This paper presents a new boundary-value problem formulation for quantifying uncertainty induced by the presence of small Brownian noise near transversally stable periodic orbits (limit cycles) and quasiperiodic invariant tori of the…

We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter…

This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…

We present an example of a linear partial differential equation whose Cauchy problem becomes well-posed when perturbed by noise. Specifically, we make clear how a suitable multiplicative Stratonovich perturbation of Brownian type renders a…

We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified…

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales,…

We consider a family of singular surface quasi-geostrophic equations $$ \partial_{t}\theta+u\cdot\nabla\theta=-\nu (-\Delta)^{\gamma/2}\theta+(-\Delta)^{\alpha/2}\xi,\qquad u=\nabla^{\perp}(-\Delta)^{-1/2}\theta, $$ on…

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…

The effect of multiplicative noise to the Turing instability of the Brusselator system is investigated. We show that when the noise acts on both of the concentrations with the same intensities, then the Turing instability is suppressed…

The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using…