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...

The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley eq...

We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the co...

We solve the rotational abrasion model of Roth, Marques, and Durian [Phys. Rev. E 83, 031303 (2011)], a one-dimensional quasilinear partial differential equation resembling the inviscid Burgers equation with the unusual feature of a step function factor as a coefficient. The complexity of the solution is primarily in keeping track of the cases in the piecewise function that results from certain...

Considering the fractal structure of space-time, a Burgers – Korteweg – de Vries (BKdV) type equation is obtained. Particularly, if the motions of the “non-differentiable fluid” are irrotational, the BKdV type equation is reduced to a non-linear Schrödinger type equation. In this case, the scalar complex velocity field simultaneously becomes wave function.

In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and ...

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.