相关论文: Structure preservation and emergent dissipation in…
The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier-Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier-Stokes equations in vorticity form; in…
A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…
We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…
A stochastic version of the two-layer quasi-geostrophic model (2LQG) with multiplicative transport noise is analysed. This popular intermediate complexity model describes large scale atmosphere and ocean dynamics at the mid-latitudes. The…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…
Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…
We investigate theoretically and numerically transport noise-induced diffusion in flows on the sphere. Previous analysis on the torus demonstrated that suitably chosen transport noise in the Euler equations leads to diffusive behavior…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…
Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise, as well as to nonlocal coupling. In this…
We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
We study the development of mean structures in a nonlinear model of large scale ocean dynamics with bottom topography and dissipation, and forced with a noise term. We show that the presence of noise in this nonlinear model leads to…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…
The stochastic $p$-Laplace equation with multiplicative transport noise is studied on the torus $\mathbb T^d\, (d\geq 2)$. It is shown that the dissipation is enhanced by transport noise in both the averaged sense and the pathwise sense.
We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…