Finite difference approximate solutions for the two-dimensional Burgersʹ system

Finite difference approximate solutions for the two-dimensional Burgers system which models a turbulent flow in a channel. Implicit Euler method is applied to obtain approximate solutions. Existence of solutions is shown by using Leray-Schauder fixed-point theorem. Stability and uniqueness of the solution are also shown by judicious applications of the discrete Gronwallʹs inequality and energy methods.