相关论文: Forced Burgers Equation in an Unbounded Domain
We study the inviscid Burgers equation in the presence of spatially periodic potential force. We prove that for foliated initial value problem there are always solutions developing shocks in a finite time. We give an application of this…
We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless…
We study the inviscid Burgers equation on the circle $\mathbb{T}:=\mathbb{R}/\mathbb{Z}$ forced by the derivative of a Poisson point process on $\mathbb{R}\times\mathbb{T}$. We construct global solutions with mean $\theta$ simultaneously…
Burgers turbulence subject to a force $f(x,t)=\sum_jf_j(x)\delta(t-t_j)$, where the $t_j$'s are ``kicking times'' and the ``impulses'' $f_j(x)$ have arbitrary space dependence, combines features of the purely decaying and the continuously…
The dynamics of the multi-dimensional randomly forced Burgers equation is studied in the limit of vanishing viscosity. It is shown both theoretically and numerically that the shocks have a universal global structure which is determined by…
The one dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed…
We consider the 1D viscous Burgers equation with a control localised in a finite interval. It is proved that, for any $\varepsilon>0$, one can find a time $T$ of order $\log\varepsilon^{-1}$ such that any initial state can be steered to the…
A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference and velocity gradient are derived. No closure assumptions…
We show the vanishing viscosity limit to entropy shocks for the fractal Burgers equation in one space dimension. More precisely, we quantify the rate of convergence of the inviscid limit in $L^2$ for large initial perturbations around the…
The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and…
We describe the asymptotic behaviour of solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the…
Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the…
Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
We prove that the viscous Burgers equation has a globally defined smooth solution in all dimensions provided the initial condition and the forcing term are smooth and bounded together with their derivatives. Such solutions may have infinite…
A rigorous study is carried out for the randomly forced Burgers equation in the inviscid limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of…
We construct a formally time-reversible, one-dimensional forced Burgers equation by imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating state-dependent dissipation coefficient.…
We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length $x$. This also gives…
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…
We study the vanishing viscosity limit of the one-dimensional Burgers equation near nondegenerate shock formation. We develop a matched asymptotic expansion that describes small-viscosity solutions to arbitrary order up to the moment the…