In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

Intermittency effects in Burgers equation driven by thermal noise. Abstract For the Burgers equation driven by thermal noise leading asymp-totics of pair and high-order correlators of the velocity field are found for finite times and large distances. It is shown that the intermittency takes place: some correlators are much larger than their reducible parts. Intermittency implies strong non-Gaus...

Optimal control problems (OCP) for Burgers equation are important for the development of numerical methods for optimal control of more complicated models in fluid dynamics such as Navier-Stokes equations. In this work, we analyze variant preconditioners for the saddle point problem arising from boundary control of unsteady Burgers equation. As for a solution approach for the discretization of t...

We derive from the Navier-Stokes equation an exact equation satisfied by the dissi-pation rate correlation function, < ǫ(x + r, t + τ)ǫ(x, t) >, which we study in the equal time limit. We exploit its mathematical similarity to the corresponding equation derived from the 1-dimensional stochastic Burgers equation to show that the main intermittency exponents are µ 1 = 2 − ζ 6 and µ 2 = 2 ˜ z 4 − ...

A stochastic representation of the dynamics of the Burger's turbulence model and of the two{dimensional turbulence is developed. The random velocity eld is regarded as a multivariate stochastic Markov process deened by a master equation. It is shown that Burgers' equation and the two{dimensional Navier{Stokes equation are obtained as the macroscopic equations for the averages of the underlying ...

We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated. Keywords—Shock, Soliton, Coupling, Superthermal ions.

In this paper, we shall use the variational iteration method to introduce a framework for analytic treatment of linearized Burgers’ equation and coupled Burgers’ equations in 2dimensional space. For these equations, the exact solutions are obtained. The paper confirms the power and efficiency of the method in reducing the size of the calculation, also the simplicity of the method compared with ...