Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

In this letter, a coupled system of viscous Burgers’ equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgers’ equation with zero Dirichlet boundary conditions, the zero equilibrium is the unique global exponential point attractor. A similar property is shown for the coupled Burgers’ equations, i.e., trajectories sta...

In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...

In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T , there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T . In addition, the global convergence and regularity of series solutions is established for initial data satisfying mil...

Scaling limits for the solution of Burgers equation are investigated. It is shown that the limiting distribution for the solution of Wick type Burgers equation with Gaussian initial data is the same as that for the solution of Burgers equation with ordinary product calculated in [LPW96].

This document provides a proof that the solutions to Convectively Filtered Burgers equation, will converge to the entropy solution of Inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of Inviscid Burgers equation. That solution is then shown to be the entropy solution.

Scaling limits for the solution of Burgers equation are investigated. It is shown that the limiting distribution for the solution of Wick type Burgers equation with Gaussian initial data is the same as that for the solution of Burgers equation with ordinary product calculated in LPW96].

The Burgers vector b with components (1.1) is teated as a vector of a special space, it is called the Burgers space. The Burgers space is an imaginary space, it is assumed to be filled with the infinite ideal (non-distorted) crystalline grid. The tensor T̂ in (1.1) is a double space tensor : its upper index i is associated with some Cartesian coordinate system in the Burgers space, its lower ind...

& Y R + Q 32 RQ 2 May, 2010 MATHEMATICA NUMERICA SINICA Vol.32, No.2 pji]\aonced^`gbfmh_ Burgers-Huxley lk*1) W[X SVU YZT (i#?*Q* , 3 200092) K F A #Q ε L Burgers-Huxley m2I3hqÆ# qX+ :8Z4 m}c, xCo Q>2(sMGk Sh Qm>. b_.m L @%, CA sinh LGk ShB Chebyshev :S[ @%8* , p&#55:S!Z=I5yG^; >.m !CoQ>2( sM 4 8 Runge-Kutta h < L{E, CrÆ s%XMe QLmh[ut > :8 Z}c>PILLQm {X c. Qm@. , xa6Lmh[ > I @% %L :8Z Burgers-H...