Limit set of trajectories of the coupled viscous Burgersʹ equations Original Research Article

In this letter, a coupled system of viscous Burgersʹ equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgersʹ equation with zero Dirichlet boundary conditions, the zero equilibrium is the unique global exponential point attractor. A similar property is shown for the coupled Burgersʹ equations, i.e., trajectories starting with initial data which is not too large, approach the zero equilibrium as time goes to infinity. This “approaching” or convergence is not necessarily exponentially fast, unlike the single viscous Burgersʹ equation.