相关论文: Transient Growth in Stochastic Burgers Flows
We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces. The equation is sublinear for large values of the state,…
We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim 1/k$, where $k$ is the wave number. From very-high-resolution numerical simulations, in the…
In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the…
We consider the weakly asymmetric simple exclusion process on the discrete space $\{1,...,n-1\}$, in contact with stochastic reservoirs, both with density $\rho\in{(0,1)}$ at the extremity points, and starting from the invariant state,…
In this study we investigate vortex structures which lead to the maximum possible growth of palinstrophy in two-dimensional incompressible flows on a periodic domain. The issue of palinstrophy growth is related to a broader research program…
This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in…
We explore a connection of the deterministically forced Burgers equation for local velocity fields with probabilistic solutions of the Schr\"{o}dinger boundary data problem. An issue of deducing the most likely interpolating dynamics from…
A "metastable solution" to a differential equation typically refers to a family of solutions for which nearby initial data converges to the family much faster than evolution along the family. Metastable families have been observed both…
In this paper we prove the convergence to the stochastic Burgers equation from one-dimensional interacting particle systems, whose dynamics allow the degeneracy of the jump rates. To this aim, we provide a new proof of the second order…
In this paper, we establish the existence and uniqueness of invariant measures for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to SPDEs…
We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
We describe a novel mathematical method to supplant the classic approach and properly treat the spatiotemporal scale disparities present between the acoustics and remaining fluid dynamics. The method is applied in this work to well-known…
The present work is devoted to the evolution of random solutions of the unforced Burgers and KPZ equations in d-dimensions in the limit of vanishing viscosity. We consider a cellular model and as initial condition assign a value for the…
Burgers' equation is an important mathematical model used to study gas dynamics and traffic flow, among many other applications. Previous analysis of solutions to Burgers' equation shows an infinite stream of simple poles born at t = 0^+,…
In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
We study the focusing stochastic nonlinear Schr\"odinger equation in 1D in the $L^2$-critical and supercritical cases with an additive or multiplicative perturbation driven by space-time white noise. Unlike the deterministic case, the…
This work is a review with proofs of a group of results on the stochastic Burgers equation with small viscosity, obtained during the last two decades. These results jointly show that the equation makes a surprisingly good model of…
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers'…